This is my try to use rete js with vue and internet explorer 11 support using babel, babel polyfill and webpack.

.babelrc

{
    "presets": [
      ["@babel/preset-env", 
        {
        "targets": {
          "browsers": ["last 2 versions", "ie >= 11"]
        }
          
      }]
    ]
  }

console.log

[Vue warn]: You are using the runtime-only build of Vue where the template compiler is not available. Either pre-compile the templates into render functions, or use the compiler-included build.

found in

---> <Anonymous>
       <Root>
warn @ vue.runtime.esm.js:588
mountComponent @ vue.runtime.esm.js:2746
Vue.$mount @ vue.runtime.esm.js:7983
init @ vue.runtime.esm.js:4128
createComponent @ vue.runtime.esm.js:5592
createElm @ vue.runtime.esm.js:5539
patch @ vue.runtime.esm.js:6114
Vue._update @ vue.runtime.esm.js:2655
updateComponent @ vue.runtime.esm.js:2783
get @ vue.runtime.esm.js:3137
Watcher @ vue.runtime.esm.js:3126
mountComponent @ vue.runtime.esm.js:2790
Vue.$mount @ vue.runtime.esm.js:7983
m @ vue-render-plugin.min.js:6
(anonymous) @ vue-render-plugin.min.js:6
(anonymous) @ rete.min.js:6
value @ rete.min.js:6
o @ rete.min.js:6
value @ rete.min.js:6
bind @ vue-render-plugin.min.js:6
callHook$1 @ vue.runtime.esm.js:6277
_update @ vue.runtime.esm.js:6199
updateDirectives @ vue.runtime.esm.js:6180
invokeCreateHooks @ vue.runtime.esm.js:5682
createElm @ vue.runtime.esm.js:5570
createChildren @ vue.runtime.esm.js:5666
createElm @ vue.runtime.esm.js:5568
createChildren @ vue.runtime.esm.js:5666
createElm @ vue.runtime.esm.js:5568
patch @ vue.runtime.esm.js:6075
Vue._update @ vue.runtime.esm.js:2655
updateComponent @ vue.runtime.esm.js:2783
get @ vue.runtime.esm.js:3137
Watcher @ vue.runtime.esm.js:3126
mountComponent @ vue.runtime.esm.js:2790
Vue.$mount @ vue.runtime.esm.js:7983
init @ vue.runtime.esm.js:4128
createComponent @ vue.runtime.esm.js:5592
createElm @ vue.runtime.esm.js:5539
patch @ vue.runtime.esm.js:6114
Vue._update @ vue.runtime.esm.js:2655
updateComponent @ vue.runtime.esm.js:2783
get @ vue.runtime.esm.js:3137
Watcher @ vue.runtime.esm.js:3126
mountComponent @ vue.runtime.esm.js:2790
Vue.$mount @ vue.runtime.esm.js:7983
m @ vue-render-plugin.min.js:6
(anonymous) @ vue-render-plugin.min.js:6
(anonymous) @ rete.min.js:6
value @ rete.min.js:6
o @ rete.min.js:6
value @ rete.min.js:6
value @ rete.min.js:6
_callee2$ @ main.js:209
tryCatch @ runtime.js:62
invoke @ runtime.js:296
prototype.(anonymous function) @ runtime.js:114
asyncGeneratorStep @ main.js:16
_next @ main.js:18
Promise.then (async)
asyncGeneratorStep @ main.js:16
_next @ main.js:18
Promise.then (async)
asyncGeneratorStep @ main.js:16
_next @ main.js:18
Promise.then (async)
asyncGeneratorStep @ main.js:16
_next @ main.js:18
(anonymous) @ main.js:18
(anonymous) @ main.js:18
(anonymous) @ main.js:246
./src/main.js @ bundle.js:3354
__webpack_require__ @ bundle.js:20
(anonymous) @ main.js:2
0 @ bundle.js:3365
__webpack_require__ @ bundle.js:20
(anonymous) @ bundle.js:84
(anonymous) @ bundle.js:87

main.js

import Rete from "rete";
import Vue from 'vue/dist/vue.min.js';
import * as vue from "vue-template-compiler";
import ConnectionPlugin from 'rete-connection-plugin';
import VueRenderPlugin from 'rete-vue-render-plugin';
import ContextMenuPlugin from 'rete-context-menu-plugin';
import AreaPlugin from 'rete-area-plugin';
var numSocket = new Rete.Socket('Number value');

var VueNumControl = {
  props: ['readonly', 'emitter', 'ikey', 'getData', 'putData'],
  template: '<input type="number" :value="value" @input="change($event)"/>',
  data() {
    return {
      value: 0,
    }
  },
  methods: {
    change(e){
      this.value = +e.target.value;
      this.update();
    },
    update() {
      if (this.ikey)
        this.putData(this.ikey, this.value)
      this.emitter.trigger('process');
    }
  },
  mounted() {
    this.value = this.getData(this.ikey);
  }
}

class NumControl extends Rete.Control {

  constructor(emitter, key, readonly) {
    super(key);
    this.component = VueNumControl;
    this.props = { emitter, ikey: key, readonly };
  }

  setValue(val) {
    this.vueContext.value = val;
  }
}

class NumComponent extends Rete.Component {

    constructor(){
        super("Number");
    }

    builder(node) {
        var out1 = new Rete.Output('num', "Number", numSocket);

        return node.addControl(new NumControl(this.editor, 'num')).addOutput(out1);
    }

    worker(node, inputs, outputs) {
        outputs['num'] = node.data.num;
    }
}

class AddComponent extends Rete.Component {
    constructor(){
        super("Add");
    }

    builder(node) {
        var inp1 = new Rete.Input('num1',"Number", numSocket);
        var inp2 = new Rete.Input('num2', "Number", numSocket);
        var out = new Rete.Output('num', "Number", numSocket);

        inp1.addControl(new NumControl(this.editor, 'num1'))
        inp2.addControl(new NumControl(this.editor, 'num2'))

        return node
            .addInput(inp1)
            .addInput(inp2)
            .addControl(new NumControl(this.editor, 'preview', true))
            .addOutput(out);
    }

    worker(node, inputs, outputs) {
        var n1 = inputs['num1'].length?inputs['num1'][0]:node.data.num1;
        var n2 = inputs['num2'].length?inputs['num2'][0]:node.data.num2;
        var sum = n1 + n2;
        
        this.editor.nodes.find(n => n.id == node.id).controls.get('preview').setValue(sum);
        outputs['num'] = sum;
    }
}

(async () => {
    var container = document.querySelector('#rete');
    var components = [new NumComponent(), new AddComponent()];
    
    var editor = new Rete.NodeEditor('floweditor@1.0.0', container);
    editor.use(ConnectionPlugin, { curvature: 0.4 });
    editor.use(VueRenderPlugin);
    editor.use(ContextMenuPlugin);
    editor.use(AreaPlugin);

    var engine = new Rete.Engine('floweditor@1.0.0');
    
    components.map(c => {
        editor.register(c);
        engine.register(c);
    });

    var n1 = await components[0].createNode({num: 2});
    var n2 = await components[0].createNode({num: 0});
    var add = await components[1].createNode();

    n1.position = [80, 200];
    n2.position = [80, 400];
    add.position = [500, 240];
 

    editor.addNode(n1);
    editor.addNode(n2);
    editor.addNode(add);

    editor.connect(n1.outputs.get('num'), add.inputs.get('num1'));
    editor.connect(n2.outputs.get('num'), add.inputs.get('num2'));


    editor.on('process nodecreated noderemoved connectioncreated connectionremoved', async () => {
      console.log('process');
        await engine.abort();
        await engine.process(editor.toJSON());
    });

    editor.view.resize();
    AreaPlugin.zoomAt(editor);
    editor.trigger('process');
})();

package.json

{
  "name": "floweditor",
  "version": "1.0.0",
  "description": "",
  "main": "index.js",
  "scripts": {
    "prod": "webpack --mode production",
    "dev": "webpack --mode development --watch"
  },
  "keywords": [],
  "author": "",
  "license": "ISC",
  "devDependencies": {
    "@babel/core": "^7.0.0",
    "@babel/preset-env": "^7.0.0",
    "@babel/preset-es2015": "^7.0.0-beta.53",
    "@babel/preset-react": "^7.0.0",
    "babel-loader": "^8.0.2",
    "webpack": "^4.17.2",
    "webpack-cli": "^3.1.0"
  },
  "dependencies": {
    "@babel/polyfill": "^7.0.0",
    "rete": "^1.0.0-alpha.9",
    "rete-area-plugin": "^0.1.6",
    "rete-connection-plugin": "^0.1.2",
    "rete-context-menu-plugin": "^0.1.4",
    "rete-vue-render-plugin": "^0.2.1",
    "vue": "^2.5.17",
    "vue-loader": "^15.4.1",
    "vue-template-compiler": "^2.5.17"
  }
}

webpack.config.js

const path = require('path');
const VueLoaderPlugin = require('vue-loader/lib/plugin');
module.exports = {
    entry: ["@babel/polyfill", "./src/main.js"],
    // entry: "./src/main.js",
    module: {
        rules: [{
            test: /\.js$/,
            exclude: /node_modules/,
            use: {
                loader: "babel-loader"
            }
        }, {
            test: /\.vue$/,
            use: {
                loader: "vue-loader"
            }
        }]
    },
    output: {
        filename: 'bundle.js',
        path: path.resolve(__dirname, 'dist/')
    },
    plugins: [
        new VueLoaderPlugin()
    ]
};