From what I understand, an ostinato should be continuous. It’s not just a riff that repeats for a bit and then there’s a chorus or some other break, it is continuous.
Well, musicologist Allan Pollack uses the word to refer to the riff in the Beatles songs “I Want to Tell You” and “Day Tripper,” where it’s a typical rock riff (not continuous through the song). The latter , though, at least continues through the sung verse (like the Stones’ “Satisfaction,” but unlike in a lot of Stones songs with notable riffs.)
But he may be stretching the term in a less serious context.