Nah. Nothing to do with Steam, should work just the same. In fact, with Proton [GE] any of the two tweaks might be sufficient on its own.

I downloaded the Japanese Rewrite trial in the meantime.

Its config utility (in ./StartData/) is called SetMovie.exe (LUNARiA has Config.exe there). It does have the MCI option (only that, in fact). Enabling that creates ./StartData/GameData/Savedata/Movie.ini with #MOVIE_PLAY_TYPE = MCI in it (for LUNARiA it's ./StartData/GameData/savedata/system.ini and #MOVIE_TYPE = 0).
The point is, Rewrite+ almost certainly has this option, by whatever name.

The most comfortable way to run another programme within the Proton prefix is using protontricks, but just creating/editing the ini should do the trick.

As for transcoding, the videos are in ./StartData/GameData/mov/. The Rewrite trial has just an MPEG there, which should not need transcoding, LUNARiA's WMVs do, at least in vanilla WINE. Proton GE may be able to play either as-is.