Rugby League 2 on Nintendo Wii? Never Released

Rugby League 2 (2005) launched on PlayStation 2, Xbox (original), and PC. A Wii version was never developed or announced.

Rugby Games That Actually Exist on Wii

• Rugby World Cup 2011 (2011, HB Studios / 505 Games) — Only rugby title on Wii.
• Sidhe's Rugby Challenge — PS3/360/PC only. Not on Wii.

Modern Rugby Games (Current Gen)

• Rugby 22 / Rugby 24 — Switch, PS4/5, Xbox, PC
• Rugby League Live 4 — PS4, Xbox One, PC

If you want rugby on Wii, Rugby World Cup 2011 is your only option. It's... functional. For a good rugby game, play on Switch or modern consoles.