I wouldn't find it too claustrophobic. The ride car has an open top, and you are then lifted up under a big IMAX dome. The sides can be a little tight depending on how many are/the size of people in your row. So, it can be a tight squeeze wall to wall, but there is head and breathing room. You are not brought very close to the "ceiling" and is quite far from you.
If you ever rode Back to the Future, it is the exact same ride car (just painted Krusty colors).