I think part of it is due to the fact that Google has greater access to a broader audience. Not everyone will search Twitter for "Donald Trump" but they will certainly search Google - so Google is providing a way for the candidates to take advantage of what is already happening probably millions of times every day.
I'd argue further that Twitter has done close to nothing to make their search a useful feature in the first place, which is why people aren't searching Twitter with "Donald Trump". If I was Twitter, this would be very worrying. All they've managed to do so far is "firehose search", which is only useful for realtime events unfolding. They probably should have been thinking about "topic search" and "person search" for a while now...
Yeah, the inability to search your Twitter feed is simply infuriating. This is an embarrassingly parallel problem, so the issue isn't scale slowing the development of Search down. Twitter just doesn't give a shit.
