The name itself doesn’t seem to match the photo. There’s a ping pong table but that itself isn’t permanent and it doesn’t look like an “arena.”
I agree that arena seems out of place for what is a room. Perhaps it’s a translation issue?
The photos do a good job of showing the location next to the pool.
Since the rejection reasons are about not understanding that it is in a hotel and that is eligible along with it being significant.
So I would tackle those.
Is there a link to the hotel webpage, does it list the table tennis facility? If there is do include that in the appeal.
It might also then help demonstrate that this is distinct in its own right.
The google have several foto showing the building. The building only have 1 room. Its supposed to be fitness center although it only have table tennis, some dumbbell and mirror. The location is good near the pool.
I actually like the title you gave. The “arena” part gives it a spark of excitement for me.
The rejection reasons are defenitely wrong, especially the private property one. I would appeal this with a link if available.
I would emphasise on the eligibility of “A great place to exercise” in the appeal notes even if it just one ping pong table with a dumbell. I have plenty of lonely ping pong tables accepted in my area. This shouldn’t be too hard to get through I find.