The speakers you've shown get wired up using standard speaker wire, I haven't come across any TV's or soundcards that actually have connections for speaker wire. Normally it's just RCA cables from TV's and headphone jack to RCA for sound cards. These are then plugged into a receiver/amp to power the speakers. You could probably hack into the tv casing to get to the internal speaker wiring however this doesn't get past the soundcard issue.
As these speakers aren't active speakers (self powerd like the speaker packages you get for pc's) you will need some source of power to drive them, I can't see any way around not having an amplifier.
Could you not put the amp with the wall mount tv? or with the pc?