Browsers need very high performance, too.
To be fair to my analogy, both ICE and Jet engines need high RPMs too, and pull power but not on the same level.
Browsers layout and rendering will have some elements similar to that of a game, but it isn't on the same level. A game can usually assume that it's trusted to run that shader, in a browser that's a vector for attack. Security design will impact game engines and browsers differently.
Granted, people are doing their darnedest to make games in the lowest common denominator technology, i.e. Electron.
C was designed to write Unix, but they didn't overfit it for that very specific case only. So it has seen application elsewhere.
Neither was Rust overfitted to exactly only writing browser engines.
> And a jet engine and IC engine are engines, but putting your car engine into a Boeing and vice versa would be an unwise decision.
Sure, but you'd expect the design software for a car engine to be at least half-way relevant for a jet engine in a pinch.
Compared to eg the software an architect would use to design a bridge.
I'd argue you're over-abstracting the differences. They have different purposes. Game engines need high performance, while browsers need to enable wide selection of APIs.