Why do EU electrical sockets/plugs have two pins for grounding?
Figure 1. Schuko sockets. (Image source: Bran.)
If you are referring to these sockets the dual earth pins give balance pressure on the plug which would otherwise be forced to upwards or downwards making insertion difficult and possibly affecting the contact of the L and N pins in their sockets.

... does this mean that in such design I could theoretically have one broken pin for grounding and successfully ground a plugged device only by using one pin on the socket?

Yes, but it is most likely that the two contacts are stamped out of one sheet of metal and there are no joints so fracture or breakage is unlikely.