(I believe this claim was made an error.) or (This is an original production and transformative work that includes fair use of footage and music originally composed and licensed for the video game. (Insert game name here) for the purpose of parody and review.)
I see somebody has seen the podcast with Fraser Agar and TotalBiscuit! ^p^
Are you sure SIAE didn't sell or transfer their exclusive rights to your songs to BFTA?
^ THIS!
That is the first thing you always need to check in such case (which you did).
Outside of that though, it HAS been happening quite a lot that companies that have NOTHING to do with the claimed content have flagged it, just go "get a piece of the pie".
If SIAE has not transferred their rights, you should counter-claim and tell them that you made those songs.
It would also be beneficial if you still had the note sheets, project-files or anything else you used in the process of making those songs, just in case stuff ever escalates, so you have actual PROOF for your claim.
It USUALLY shouldn't come that far, especially if you ARE the original writer and didn't use any pieces from anywhere else, but you never know. Some companies can be jerks.
PS: Great to see fellow Italians in here. =)