Why does a "senior" developer have a git repo for a critical application that makes our company money, never push to it? I checked it today and it's empty.

If they're like one of my coworkers who does something similar, their head must be too far up their ass to read the commit message.

My guess: he wanted to use git but didn't got along with it. After a while he gave up and used Dropbox or svn as CVS. There's probably another repo somewhere else

Either he doesn't know what he's doing or he wants (wrongful) job security.

Either way he should be confronted. Imagine what would happen to the company if he:
A) dies
B) quits
C) his hard drive destroyed beyond repair (assuming he never pushed to anywhere, not even a personal remote repo)

@develrant this guy knows what's up.