It would certainly be a lot more of a niche hobby. I think after the crash of 1983, companies would have focused less on consoles and more on arcade games and PCs. Perhaps Atari or Sega would have given console gaming a try, but I don't either would have been as successful as the NES.
Also, without that deal that went sideways with Sony, the Playstation never becomes a thing, and Microsoft would have just settled for being full-time PC.
As far as the games themselves, they would have been radically different. Think about how many game devs were influenced by Nintendo in some way.