While we're on the subject of the pinned queen, consider a few other positions where it can't bite back against the piece that pins it. These studies don’t involve cross-pins, but they are similar in important respects: in each of them you have the queen pinned; and if it captures your pinning piece, you achieve mate or some other decisive gain.
The most salient facts of the position pictured here are two: the alignment of Black’s king and queen with nothing between them on the g-file, creating the kernel of a pin; and the coordination of White’s queen and d7 rook, both trained on f7 and almost able to deliver mate with Qxf7. (Anytime your queen can land on a square next to the enemy king and get backup from one of your other pieces, you have a threat worth exploring.) A pin against Black’s queen would need to be delivered vertically by White’s queen (which can’t get there) or his d4 rook (much better anyway as a pinning tool, of course, because it’s cheaper). A piece that tries to pin the queen usually needs protection, and the rook would find none on g4. But it sometimes is the case that a queen pinned to its king is performing important defensive functions that constrain its ability to lash out at a piece that pins it. That is so here: imagine Black playing QxRg4 and see that Qxf7 would have a new significance, attacking the king not only with protection but without any Black guards to worry about. Black’s king would have nothing to do but move to h8. White then would have a crushing queen-and-rook battery on the seventh rank, allowing him to play Qxh7#. So Black’s queen wouldn't be free to take the rook that pins it after all, and Rg4 therefore wins.