I looked into it further and honestly, what a trouble - if you look at the old GMEZ, it has two sets of GMLive executables - one in datafiles/ (old version?) and one in datafiles/GMLive/ (right ones), but GMS1 imports the top-level ones instead. And not just that - if you try to re-export the extension afterwards, it somehow grabs those old files even if you deleted them from the project folder. Truly amazing.
I manually removed them from GMEZ (which seems enough to fix this) and reuploaded.