I will agree that this does not look like classical bagua.
Fairbairn himself goes only so far as to credit "Chinese boxing" as one inspiration or ingredient in his system. It's been plausibly suggested that the Chinese boxing he learned was Yin Fu bagua, but I don't see clear stylistic clues to that. What he is doing here does not look like Judo atemi either.
Perhaps when the different ingredients went into the stew, some of them lost their characteristic flavors, in favor of an unembellished, very direct and mechanical way of moving. We know that the emphasis was on techniques made easy to teach and to learn. Fairbairn's liking for messing with the opponent's spinal geometry, though, seems to me more characteristically Chinese, at least in inspiration.
I define internal martial art as unusual muscle recruitment and leave it at that. If my definition is incomplete, at least it is correct so far as it goes.