There is no mainline Final Fantasy game starring Cloud Strife released on PlayStation 2. Final Fantasy VII launched on PS1 (1997); its direct sequels/prequels skipped PS2.
This is a CGI movie (2005), not a game. Released on DVD/UMD (PSP), not as a PS2 game disc.
If you want to play as Cloud on a Sony home console, Kingdom Hearts I/II on PS2 (or PS3/PS4/PS5 collections) are your only PS2‑era options.