I know this post is only going to be relevant for a couple of weeks, but today I tried to launch StarCraft Remastered under WINE and it crashed.
Pertinent info: StarCraft Version 126.96.36.19926 WINE version 4.20-staging Battle.Net version 188.8.131.5298
Fix was to open the Battle.Net settings -> Game Settings -> "Launch 32-bit client (instead of 64-bit)"
Apparently the 64-bit version has become the default sometime since I last played it (October?!): https://us.forums.blizzard.com/en/starcraft/t/enabling-64-bit/458/7