I'm not entirely sure what you mean by "game engine" here.
Maybe I meant both back end and front end?
- High performance server code handling continuous multiple requests
- Rendering engine and game logic
Those are very different things; on the client side I wouldn't write my own considering how many are already out there, and they're battle-tested and good. On the back end I'd caution against making a premature choice based on what you think will happen: there are many options, most of which will handle most of what people write. Only real advice is to go for something that scales horizontally.