Then why is he referenced as "Commander" for rank?
The reason was mentioned previous. Per regulations, the officer doing the promition ceremony has to be of a higher rank than the officer being promoted. So sometimes the lower ranked officer is temporarily pinned to be a higher rank than the officer getting the promotion. It for apperances. Just like an Army Captain will be addresses as Colonel aboard a navel vessel. There can only be one Captain on a ship.
Why would you call an Army Captain "Colonel" when Colonel is 3 grades ahead of Captain, which is equivalent to a Lieutenant in the Navy? It would be more appropriate to call him or her "Lieutenant."
BTW, I was in the US Army for 4 years and I've seen peoples' family members pin on their ranks, I've seen a Sergeant First Class pin Captain's bars on a former Lieutenant or 1st Lieutenant onto a former 2nd Lieutenant.. It's not always a person of higher rank who pins on the rank, it's usually a person in the officer's chain of command or family. (Jake Sisko also pinned the Captain's pip onto his father's uniform on DS9) In the case of the Sergeant First Class, they are usually Platoon Sergeants and Lieutenants are Platoon Leaders. (in name only) The real leader of the platoon is the NCO, the officer is there because they're fresh out of training and need to learn from somebody with a lot of experience.
As for the rank on the guy in the game, the most likely answer is that it's an error. The writers wrote a Commander but the graphics artists made a Fleet Admiral. The other option is that he is a Fleet Admiral and he's Commander Starfleet, like Admiral Morrow was in Star Trek III. However, that's unlikely as Admiral Quinn is probably Commander Starfleet, so I'll still go with the error.
I think you got your Rear Admirals mixed up, but that's basically it.
I miss Commodores. I always thought Commodore sounded cool, much better than Rear Admiral Lower Half. Just because the US Navy went to that system didn't mean that Star Trek had to. After all, TOS was in the 23rd century and they had Commodores back then (because the US Navy had them back then also.) However, they could have brought the rank back in the future.
Maybe the officer is referred to as Commander, because he's the C in C (Commander in Chief) of Starfleet? Or is Admiral Quinn the C in C, since he has the same rank as Admiral Hilo? According to the STO wiki, Menn Hilo might be Starfleets C in C.