In the main BT studio then. Do BT produce this for them?
It's the main studio used by BT Sport that Timeline operate. BT use a lot of Indies to produce their own content - though I think some is in house - and it's unlikely BT would produce content for the BBC (unless it was a shared show)
AIUI the BBC NFL Show continues to be produced by Whisper TV (who have a strong relationship with Timeline through their Channel 4 F1, SailGP etc. productions) I think previously the show came from a smaller studio at Timeline/BT's Stratford studios - but I guess social distancing (both in front and behind the camera) means using the larger studio makes sense at the moment?
I think it's just because it was the Thanksgiving special.
They usually seem to record it earlier in the week, then just slot in the Thursday night highlights (crucially compared to the other games, there is no analysis).
But with it being Thanksgiving and the original intention of having 3 games on the Thursday night (only two were actually played due to the Baltimore Ravens/Pittsburgh Steelers game being called off due to the Ravens having 20 players on the COVID list), they may have recorded it on the Friday and the usual studio may not have been available.