I see a lot of intermediate+ / advanced recreational players hit deceptive cross-court drop shots.
Better doubles player in defence position biased to the long line side on lifts, so the cross court side open. This isn't a real problem, because cross court shots, travel longer and give more time to react, smashs are flatter and less powerful. In this scenario a deceptive cross court drop can be an option to exploit this area.
On the other hand many recreational players and hobby players can be obsessed with cross court shots and don't position well. I don't know which case we have.
Isn't this type of shot an attacking shot?
Any shot which force the other side to take it below the tape/not hitting is downwards is an attacking shot for me.
Why none of the players move up to follow?
Imagine, which options the defending can play in this situation. If they do a straight net, the partner can rush forward, if they lift straight, he can move to the back and attack. If they reach early the drop shot or the quality is not good they can push. So standing in this situation side by side is better cause court is vulnerable and open in whole width.
The idea behind this is the wedge attack. Here the visual explanation:
Doesn't this go against general doubles rules?
Against which rule? In doubles there some guidelines but nothing set in stone. Lower level doubles think simple that if the others are in defense one covers the whole net, the other the whole rear which can work for them. When you play longer against better opponents you will discover that the defending pair is not only able to play blocks to the net or high lifts.
They are able to play much more options and are able in defense to use the whole court better to counter, because they can move more efficient, reach the shuttle earlier, read the game, are more skilled and so on. So just standing front to back in some situations can leave more gaps even during attack.