twitter-html5-player.user.js

// ==UserScript==
// @name         Twitter HTML5 Video
// @namespace    https://venipa.net
// @version      0.1
// @description  try to take over the world!
// @author       Venipa
// @match        https://twitter.com/*
// @icon         https://www.google.com/s2/favicons?sz=64&domain=twitter.com
// @updateUrl    https://gist.github.com/Venipa/74a751f64699a9a1f25b8548d1615bd6/raw/twitter-html5-player.user.js
// @grant        unsafeWindow
// ==/UserScript==


/* jshint esversion: 6 */

(function() {
    'use strict';
    function checkVideo(video, play) {
                if (!video.controls) video.controls = true;
                if (video.style.zIndex == '') video.style.zIndex = '99';
                if (video.volume == 1) video.volume = 0.1;
                if (play) video.muted = false;
    }
    (function(video, check){
        var fn = video.load;
        video.load = function() {
            if (this.hasAttribute("playsinline")) {
                check(this, false);
            }
            return fn.apply(this, arguments);
        };
    })(unsafeWindow.HTMLVideoElement.prototype, checkVideo);
    (function(video, check){
        var fn = video.play;
        video.play = function() {
            if (this.hasAttribute("playsinline")) {
                check(this, true);
            }
            return fn.apply(this, arguments);
        };
    })(unsafeWindow.HTMLVideoElement.prototype, checkVideo);
})();

Userscript: Script
Better Twitter Player: