There's nothing computer-specific in the code above, apart from the location of the Access file, but the absence of that wouldn't produce the error above. So I think the problem must lie in your .mdb database, and I suspect the issue is that it contains tables that are linked to a SQL Server which only code running on your machine can get to.
I would troubleshoot this by using the Microsoft Access UI to open the access database on one of the other computers, opening the Employee table and seeing if you still get an error. If you do, you'll know that it's the Access database that's at fault rather than your code. I would guess at this point that remote connections are not set up on SQL Server Express (see here to find out how to enable remote connections), or some firewall rule on your machine is preventing other machines from connecting to the instance of SQL Server Express, so I'd open Windows Firewall and allow inbound traffic on the port that SQL Server Express is listening on, or (better) move the SQL Server from your local machine to a dedicated development server.