How to get the Steam Monster mini game started?

With the recent Steam Summer Sale, they introduced a Steam Monster Mini game, where you can level up and get some additional extras in the sale.

Unfortunatelly, it appears that it won't start for me. It doesn't matter whether I join a friend's game or create a new one. The game loads (x/97) and then shows this screen:

As you can see, it appears to me that the game is loaded, but won't start. There is no object moving, clicking doesn't do anything.

Is this a known problem and how can I solve it to get the game running?