Part of it also is that Giphy has licensing agreements with media rights owners to create gifs based on their content . . . they're not just indexing existing gifs.
They also have deals with twitter/Facebook so if you use a GIPHY URL it's embedded in the post. All other gif hosts get a static image.
I think it's a clear case of using "can't" to say "doesn't bother to because it's not worth it". In fact, I wouldn't be surprised that Google had great indexing of GIF already, but doesn't fully expose it in its search engine.
Their keyboard (Gboard) has GIF searching functionality already - so it's certainly something they've implemented.