I don't remember any minigames from TS2 so you'll have to forgive me for my lack of knowledge, but on the dolphin wiki someone says this:
"Arcade mode crashes as soon as the first match ("Adios Amigos!") finishes loading (tested twice). Challenge mode works a bit better, I could complete "Pane in the neck" and "Bricking it" but loading the 3rd one ("Stain removal") crashed (tested once). Tested with default settings and DSP HLE."
Sorry if it's not related to the minigames you're mentioning though, it might still be worth it to check the wiki page for it though.
"NintenDON'T sue me please haha"
Hello! Just to let you know, at least the Anaconda minigame doesn't work in Timesplitters 2. I suspect that the other minigames won't work either. All I get when I begin a game of Anaconda is a blank screen that soon goes to "game over". The rest of TS2 works fine for me.