To be fair, the museum did put a note on the chair, and put it up on a pedestal. I think that's clear enough. At that point I think their responsibility to signal that it's art has been met.
Also, the museum-goers were pretending to sit in the chair for photos, and slipped. It's clear they understood it was art.
I suppose the museum could be criticized for not doing even more to keep the chair safe, but ultimately vandals gonna vandal. The more you separate the art from the audience, the harder it is for the audience to engage with the art the way the artist intended - or even at all. My understanding is that the Mona Lisa is so far separated from the audience these days that it's hardly worth trying to engage with.
Sometimes you just have to put the piece close enough for the audience to engage with it, and hope for the best.
And sometimes, I think, you just have to accept that if this is how the audience wants to engage with it, that's part of what makes it art.