Looking at the first photo above, it looks like the chain is currently resting on top of that guide tab.

I'm having troubles imagining how the chain could or would have popped out of the proper chain routing.

Inspection of the derailleur should indicate whether there is wear on the top side of the tab.

One can ride the bike just fine with the incorrectly routed chain, but it will cause the chain to sound a bit noisier than normal.

I can't say that would have definitely caused the bike to eat the derailleur, but if the chain was, in fact, routed incorrectly, then a large part of the blame would have to fall back on the shop.