So there may be hope... Glad to hear, looking forward to your investigations, thanks!
When looking at RotT-Win32.exe I saw that Unity engine has a workaround for checking whether InitializeCriticalSectionEx is present, so I guess, this may be a bug of UnityEngine.dll and the IAT import of this function just "slipped in". I guess it should be reported to UnityEngine vendors as I think it is unintentional.
As for the patch: Check IAT entry at raw file offset 0xF9730A reading "InitializeCriticalSectionEx". Just overwrite the "Ex" part of this string with 0x00 bytes so that it reads "InitializeCriticalSection". As the function takes 3 parameters, not one, you need to patch the 2 PUSH instructions of second and third parameter at raw file offset 0xD4FD91: 6A 01 6A 00
NOP then out by putting 90 90 90 90 in there and you are done. I can upload patched file, if needed or a patcher, if you prefer, but as you see it's very easy to patch.