Junior, here's an answer from the Twilio Video team.
We aren’t investing time in Cordova/Crosswalk right now, although some customers have been asking for it on our GitHub project (https://github.com/twilio/twilio-video.js/issues/85).
twilio-video.js can be integrated into an Angular app easily today. We have a minimal framework test in our GitHub project showing how to set it up (https://github.com/twilio/twilio-video.js/tree/master/test/framework/twilio-video-angular). This isn't a full-fledged application; instead, it's meant to ensure we retain compatibility with Angular as we develop twilio-video.js. It might be nice if we had a more full-fledge Angular Quickstart application in the future, but it gets difficult to support and maintain the various different front-end frameworks (Angular, React, Ember, Meteor, Vue, etc.).
I don’t know much about Construct 2, although it looks like a commercial game engine built on JavaScript/HTML5.
Can I embed Construct 2 games into an Ionic view or simple DOM element and then render the video chat over it?
Yes, this would work.
Or, should I be integrating the WebRTC chat sessions into Construct 2?
This might work, too, assuming Construct 2 allows arbitrary JavaScript inside the game engine.
Or can I simply display both canvases in the same page?
Yes, this would work.
The technique used will depend on how much interaction between the game and the video chat needs to take place. For example, if the lifecycle of the video chat should correspond in some way to in-game elements, then it should be created within Construct 2. If the video chat serves more like a commentary on the game, separate from the gameplay mechanics, then either overlaid or alongside in the same page should work.