In a classical definition, a genus supplies what is shared and a differentia distinguishes one species from others. Such a definition presupposes a broader field of comparable kinds.
If God were defined that way, a genus containing other possible members and a distinguishing species-character would be implied. That would conflict with divine incomparability and necessary existence.
However, sharing a word does not prove sharing the same quiddity. Both God and creatures may be called “existent,” but the common word does not establish identical modes or natures of existence.