[Suicide Junkie]

But I got the idea from Fallout Tactics, were the real time combat uses action points for firing, reloading, etc.
They just left the movement out. A mistake, me thinks.

Not really.
In turn based mode, moving takes up action points.
In realtime mode, the character's movement uses up action points at the same rate as they recharge, and the speed on screen is scaled appropriately. Just makes things more convienent for the user to read the status, and avoids fractional AP usage.