Playstation did get lucky, but only in the sense that both SEGA and Nintendo screwed up with their consoles. These screw ups left an opening for a newcomer that did things right, and Sony's smart decisions with the Playstation exploited that.
Anyway, if Playstation weren't around, than either SEGA, Nintendo or Microsoft would gave filled the void. If you mean the original Playstation, developers would have simply needed to work with N64's cartridge limitations and learn to work with Saturn's difficult hardware. Both the Saturn and N64 were successful in different regions; N64 in America and Saturn in Japan, so the industry certainly could have gotten buy without PS1.
If you mean PS4, either Xbox One or Wii U are more than capable of filling in for PS4. Xbox One may have needed a price cut first, but afterwards I'm sure anyone who wanted a next gen console would go for it.
An entire industry viable industry wouldn't fold over the absense of one competitor, especially when there are so many others trying to compete. This is kind of like how peopel say Nintendo rescued the American gaming industry, when there are many other companies that would inevitably have tried to fill in the gap left by Atari, like SEGA or NEC. Certainly, Nintendo was the first company to have the balls to do it and the intelligence to do it right, but America was too big a market for these other companies to ignore forever.
