I don't hesitate to put that throw among the best I've ever seen, because I've long had fellow right fielder Ichiro Suzuki's throw to nail Terrance Long at third base in a game between the Mariners and A's in April 2001 on that list, and watching the two of them, I'm convinced that Puig's throw was better. Both were no-hop strikes to the front of the bag on runners of similar quickness going from first to third, but Puig was deeper in right field when he made his throw and, if it's even possible, his throw was more on the money.
Curiously, the Suzuki throw came in just his eighth major league game, while Puig's on Saturday night came in his sixth. It's entirely possible that the thrill of the new played a part in the amazement that greeted both throws and the fact that the latter is so well remembered more than a decade later. This very similar throw by Jeff Francouer from August 2011, for example, is every bit as impressive (particularly given that Francouer has to head in the other direction to field the ball and where third baseman Mike Moustakas catches the ball), but hasn't had the same staying power in the collective consciousness.
Still, the only other throw from right field to third base that I can think of off the top of my head that rivals Puig's from Saturday night is this one from a Yankees-White Sox game in 1993. The right fielder in question is one to whom Puig had already drawn many comparisons even before his throw on Saturday night:
And to think, just a few nights ago, we thought this was impressive.