The simple answer (from the episode...sort of)
The Anti-Time Future was supposed to happen as it was how the original timeline played out. Picard altered events significantly when
he shared his experience of how the future was going to unfold with the crew. He caused them to make different life choices, which created new future for the prime timeline
So the Anti-Time Future DID happen. In parallels, we learn of the existence of a multi-verse with a new reality created every time a choice is made. The anti-time future was one such reality but Picard made sure they didn't live it. Similarly, Picard changed the future in Time Sqared ensuring the Enterprise was not destroyed.
A Purely Specualtive Answer
The Anti-Time Future was a construct created by Q. For years, Q had been plaguing the Enterprise and Picard. In many of these cases, he would whisk the crew or the captain away to some far off place that might not have existed outside of Q's own mind (the court room, the planet with the pig soldiers in Hide and Q and Sherwood Forest for example) and only rarely sent the crew somewhere "real". In Tapestry, Picard encounters Q at the moment of his death and is taught a valuable lesson but is left to try to figure out (a) Is Q God (b) was it an elaborate test/lesson set up by Q? (c) did God appear to him in the form of Q or (d) did he imagine the whole thing?
If we go with what we are given in the episode (All Good Things...), it seems Q is testing not humanity but Picard himself. That said, it's entirely possible that the Anti-Time Future was not a possible timeline but simply a construct in Q's cosmic sandbox designed to push Picard to the point of breaking or expanding.
Either way, if it never happened, there's no conflict with the events of the movies (Data's Death, the destruction of the Enterprise D, Worf leaving Starfleet etc.)