Main reason I would say say here is due to position. A♦J♦ is a strong hand, and strong on this board, however it is not necessarily strong enough to to withstand a lot of betting pressure. The fact that A♦J♦ is out of position, means that it can easily be forced to fold and not realise their actual equity.
Let me give you an example. Let's say we make it 65-80% of pot on the flop, after all we want to charge draws. Then the turn comes a heart or a straight completing card, I will also add there is a straight already out there. If we consider our opponents range, in general the BTN can play a wide range, and there are a lot of cards that come on the turn that we don't want to see, that can easily be in a BTNs calling range. I would personally say the check here is a pot control exercise. Essentially there are a lot of bad turn cards, and pretty much the majority of them will improve the BTNs calling range.
We hate when we make it 65-80% and we're called and then a 9, Q, K, A or a heart peels off on the turn. It puts is in a really difficult spot. Similarly if we make it too small, those hands will almost certainly 3-bet us or float to see a turn. A♦J♦ vs AQ off on this 8♦J♥T♥ only has 57% equity against 40% with a small chance of a chop. Essentially by betting we really only set us up for two likely outcomes, we're going to win a small pot, or we're going to hate the turn and likely relent to pressure because we're out of position.
Checking controls the pot size and makes it much easier to evaluate a safe turn and make a likely safe river bet or call off one.
I would also say it's rather important to consider the player on the BTN. Doug Polk plays at a level both in ability and stakes that chances are none of us will ever play at. It's worth considering that he is doing this as an exploitive play because he understands his opponent better than we do in the situation. One thing that is important to take away is that in general those rules, Category 1 and 2 hands, etc are guides and not absolutes. Poker is a game where people do not play perfect and do not play GTO. Players like Polk are experts at exploiting people and this very likely was factored in to his decision as well.