Large game engines consist of many medium to large software libraries stitched together. What you're likely to see is that each such library is gradually either rewritten or replaced by Rust code, with an FFI compatibility layer matching the existing ABI where possible.
There's no reason to think that current game engines will have their fundamental APIs around scene management, serialization, entity composition, and so on, ported directly to Rust, because these things are typically designed around available language features. For example, an engine written in C++ might have its own version of `dynamic_cast` and RTTI, and that's going to be an extremely awkward design in any other language.
I think 15 years is too high, but I agree that it will be a while, because a triple-A game engine is a huge investment.