I don't think it is just the computers. The training environments and systems for learning advanced quite far without the engines. Kasparov didn't train with computers in his prime and he is still very strong by modern standards. More children were encouraged to pursue chess...in the 19th century many people (such as Paul Morphy) would consider a professional chess player in roughly the same social tier as a professional gambler. If you look at many of the games from that era it seems like only 20 people in the world even knew how to play chess.