Gotta give the poor boy props for at least protecting her dignity somewhat, even if it's but utterly destroying his.
But that's the point... he's a boy, running around shirtless is no big deal for him...
normally. Only if he's accepted her premise, which is that his boobs are an intimate zone which shouldn't be seen by everyone, is he suffering any kind of embarrassment.
That said, if I were writing this, I would have had Rika change her mind about the handstand, and just peek down his shirt. His boobs are only for her, after all!