Check the version number shown in the main menu, under the column of buttons. Someone in the GOG forum reported a problem with co-op where one person had the version number just listed as 'v'.
Please email supportdos@larian.com, with a description of the problem and the report.zip file generated by the
D:OS support tool (for the PC version) for both computers. The report will contain system and network information, any crash dumps, and your saved games (which are not relevant in this case, so can be deleted to reduce the file size, if that is an issue).