I would definitely call this a shuffle. I think of swing as having the dotted note pattern only on two and four. Shuffles have it on all four. All shuffles contain the elements of swing. I suppose there are as many definitions as there are drummers. The Rosanna/Purdie/half-time shuffle is different altogether.
Classic horn figure comps on the snare , very elegant . Old school wrist control and sitting posture . He came out of a fairly traditional jazz background and was able to put those abilities into a pop context , giving it sophistication . Panama Francis and a few others made successful careers for themselves this way . Dynamic control and balance , understanding how to bring out the drumkit's differing textures and voices . His knee is bopping up and down and I doubt that's equal fours onthe floor .
That Fred Below clip IS a wonderful feeling shuffle alright.
In my own personal world, shuffles (and brushes) are their own art forms. I can halfway play a few different shuffles but my brush playing sounds like throwing a loose ream of computer paper up in the air during a stiff wind.
Picture your hands as tennis players with the bass drum as the net . Lobbing the ball back and forth , giving it a spin here and there , rebound off the sweet spot on the racket , effortless . Ball's always moving , bouncing once , sometimes from midair ... count the tune off for the serve . Drummer's eyes in the audience watching this back and forth . Hihat foot's the chair umpire , letting me know when something's landing outside the court lines .
Shuffles in my opinion are undefinable. In this example the band is shuffling for sure, the drummer's take on it is a little different but fits great. I was watching a drumeo video of I believe Latham doing shuffles and a viewer comment was "can you demonstrate a country shuffle?" He proceeded to play what I call a train beat. That's not what I would call a country shuffle or anyone that I play with but maybe in his world it is. I've also heard some call the two handed groove on Rock and Roll a shuffle again not what I'd call a shuffle but in some circles maybe so.