They appear to be doing it in the Delta club -- or whichever the one is that's behind home plate on the 100 section.
Based on the video I saw on NY1 of them setting up the venue, it's the Ford Field MVP Club (located behind home plate in the 100s). Delta SKY360 Suite is in the 200s.Been awhile since I've been in the stadium so I forget which entrance Delta is, but the vaccine area is Gate 4 at the corner of 161 and Macombs Dam Br Ave (before it turns into Jerome near Gate 2). They've also opened some of the ticket windows up to schedule appointments because people were coming without one. So far open every day from 8am-8pm, handling up to 15,000 appointments per week. The capacity is based on vaccine availability, not what they can actually handle. They'll open it up 24/7 if they can get enough supply (Gothamist: De Blasio, Seen In Rarely Worn Bombers Cap, Launches COVID Vaccine Site At Yankee Stadium)