This works!

application.template.hbs

{{#link-to 'my-route'}}Route with action{{/link-to}}
{{outlet}}

my-component.component.js

import Ember from 'ember';

export default Ember.Component.extend({
});

my-component.template.hbs

{{my-second-component approve=(action attrs.bet 2)}}

my-route.controller.js

import Ember from 'ember';

export default Ember.Controller.extend({
  actions: {
  	bet(id, text) {
    	this.get('target').send('bet', id, text);
    }
  }
});

my-route.route.js

import Ember from 'ember';

export default Ember.Route.extend({
  actions: {
  	bet(id, text) {
  		console.log('Route!', id, text);
    }
  }
});

my-route.template.hbs

{{my-component bet=(action 'bet')}}

my-second-component.component.js

import Ember from 'ember';

export default Ember.Component.extend({
  approve: null
});

my-second-component.template.hbs

<button {{action approve 'text'}}>bet!</button>

router.js

import Ember from 'ember';
import config from './config/environment';

var Router = Ember.Router.extend({
  location: config.locationType
});

Router.map(function() {
  this.route('my-route', {path: 'my-route'});
});

export default Router;

twiddle.json

{
  "version": "0.4.13",
  "dependencies": {
    "jquery": "https://cdnjs.cloudflare.com/ajax/libs/jquery/1.11.3/jquery.js",
    "ember": "https://cdnjs.cloudflare.com/ajax/libs/ember.js/1.13.10/ember.debug.js",
    "ember-data": "https://cdnjs.cloudflare.com/ajax/libs/ember-data.js/1.13.13/ember-data.js",
    "ember-template-compiler": "https://cdnjs.cloudflare.com/ajax/libs/ember.js/1.13.10/ember-template-compiler.js"
  }
}