That appears to be a Midway cocktail cabinet, though the stuff at the bottom doesn't match their usual engineering (they usually have the parts on a wood board that can be unscrewed and removed for servicing).
Anyways, the cap thingy is most likely an AC filter. The big transformer is a transformer. Most likely an isolation transformer. Why you have two in there, I don't know. The monitor needs one. Sometimes a second one was added for redundancy just at the point where the AC line in from the external socket comes in. (For example, in Ontario, in the 70's and 80's Ontario Hydro required them and supplied them, but yours doesn't look like an Ontario Hydro one).
If it works, leave it.