While the Xbox was built with Xbox Live integrated, the PS2 required a separate network adapter for online play, making the multiplayer-only nature of CS a harder sell for casual console owners.
In the early 2000s, Valve did venture into the console market, but primarily focused on Microsoft’s Xbox. The original was a significant release that featured bot play and Xbox Live support. The PS2 was largely skipped for several reasons:
GustavoFurtad2/CounterStrike-PS2: Recreation of ... - GitHub
Counter-Strike 1.6 , often cited as the definitive version of Valve’s tactical shooter, is a cornerstone of PC gaming history. Yet, for decades, fans have wondered: why was there never an official "CS 1.6 PS2" release?
Compared to the Xbox, the PS2 had less RAM and a more complex architecture that made porting PC-centric GoldSrc engine games difficult.