1-hour MVP.

Makefile

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+fx-build:
+	web-ext -a . build
+	rename -f "s/\.zip$$/.xpi/" youtubecinema-*.zip

background.js

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+// Be compatible with Chrome|ium. We do not need the full webextension-polyfill.
+if (typeof browser === 'undefined') {
+  this.browser = chrome
+};
+
+var urlPattern = /^(https?):\/\/(?:.+\.)youtube\.com\/watch\?.*v=([^&#]+)/;
+
+function onBeforeRequestListener(details) {
+  var match = details.url.match(urlPattern);
+  var scheme = match[1];
+  var videoId = match[2];
+  if (scheme && videoId) {
+    // Watch the embedded version instead. And without related video suggestions!
+    var newUrl = scheme + '://www.youtube.com/embed/' + videoId + '?rel=0&autoplay=1';
+
+    // From the embed, one should be able to follow the "watch on YouTube" link
+    if (newUrl === details.originUrl)
+      return
+
+    return {redirectUrl: newUrl};
+  }
+}
+
+browser.webRequest.onBeforeRequest.addListener(
+  onBeforeRequestListener,
+  {urls: ["*://*.youtube.com/watch*"]},
+  ['blocking']
+);

manifest.json

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+{
+    "name": "YoutubeCinema",
+    "version": "1.0",
+    "background": {
+        "scripts": ["background.js"]
+    },
+    "permissions": [
+        "*://*.youtube.com/*",
+        "webRequest",
+        "webRequestBlocking"
+    ],
+    "applications": {
+        "gecko": {"id": "youtubecinema@youtubecinema"}
+    },
+    "manifest_version": 2
+}