Even though you cannot know that the games shown were actually played by other players, each individual player can be sure that his or her own games are correctly shown on that page. As such, if any player notices that his or her own games are not correctly shown, that player can raise a red flag and alert the community.
I think the point is that you could easily add in a bunch of imaginary winning games to make it look like on average the site is performing as advertised. Nobody could prove that the added games weren't real.
It's still interesting to see the list of recent games. I just don't think it really proves anything. (Not like your provably fair hashes do).