One of the unconventional elements of the Forge Engine RPG is the structure of the turns. Traditional RPGs have a round/turn structure where each character has a discrete turn within each round. Their actions occur within their own turn, and time passes in a strangely linear fashion which requires some mental gymnastics to unravel. Once each character's round is over, play passes on to the next character in the initiative order, etc...
The Forge Engine's combination of an Energy action economy and a system of actions and reactions that are individually costed means that the traditional linear round structure can be replaced with a more non-linear 'do what you want as long as you have the Energy' structure. Characters can jump in and out of the action as long as they have enough Energy to perform their action; whether it's moving, attacking, reloading, or some other costed action.
As with any system, there are several caveats. First, characters can take reactions before their first turn in combat, but they can't take actions. Second, if a character is surprised, they can't take actions or reactions until their first turn, which means that they can't spend Energy to dodge when they're being attacked.
(Dammit, that should be 'Character #2' up there, not Character #3...)
So, what other RPGs have non-traditional round and turn structures for combat?