Yep, that would definitely cause that error message.
You didn't answer the question I asked about if the two computer are using the same version of Excel or not. Sometimes, if you create some VBA code or a newer version and try to run it on an older version, it won't work because you may be using newer features that weren't available in the lower versions. If creating Excel files for multiple users, I always recommend writing it on the oldest version of Excel that any of your users will be using.
In any event, here are some articles that may have you resolve your missing library:
MISSING: Microsoft Windows Common Controls-2 6.0
Missing References In VBA