Yes it's impressive how the PSX took over a market previously dominated by Sega and Nintendo, but this didn't happen right away, this actually took plenty of time. Currently I view the PS3 as being in somewhat a similar position, first an impressive games library has to be build up and this seems to be happening faster than was the case for the original PSX. With unique games and functionalities Sony will have to pursuade customers to spend those extra bucks, but the must have game projects have become huge to develop, requiring multi-million dollar investments and often span years of development time. Rome wasn't build in a day.
Also note that when the PS2 was launched it was initially being outsold by the cheaper PSOne for the year. The same is currently happening with the PS3, for 2006 the much cheaper PS2 not only outsold the PS3, but the XBox 360 and Nintendo Wii as well.
Are you aware of how Sega and Nintendo both screwed up at (pretty-much) the exact same time which gave the Playstation the opportunity to take over the market?
Sega took their success with the Genesis and released the unpopular Sega CD, quickly followed that with the unpopular Sega 32x which they then followed with the Saturn which sold for $400 ( $525 with inflation ) and had 0
Nintendo took their success with the SNES and Gameboy and decided to produce the (amazingly) unpopular Virtual Boy, then Nintendo started playing around with the idea of changing licencing terms to have less crappy games on their system (even the suggestion of which offended third-parties), then they let the Saturn and Playstation battle it out for 18 months before they released the N64 (a system which was powerful but underperformed because of low memory and dramatic bottlenecks).