Is Battle Heat a turn-based fighter??...

[oldschooldave]

That's certainly what it looks like in the short gameplay footage I just viewed on this site.  Diddo with Tengai Makyo Karakuri Kakutoden.

[Kaminari]

This is more like real-time video branching

[PCEngineFX]

It's more semi-turn based.  Whoever presses the button for a move goes first, then the other person has the option to block the attack, get out of the way, or counter it.  For Tengai Makyo, the moves are a LOT slower in execution and thus not as fun as Battle Heat but is the same concept.