It also seems a bit like a Fire Emblem or FF Tactics type game
I guess I should point out that NHL games are real-time. They are, in fact, a real time tactic type of game in their own way. I haven't seen many other similar implementations of such a gameplay aside in sportsgames.
That said, if there's any hybrid (tactic game vs sportgame realtime tactics) I'm all ears.
What I was thinking was that since the combat/sports part is a separate game phase from the management, it seems easy to mentally hybridize the two. But no I've never personally encountered a non-sports real-time tactical game. There apparently are some - when I googled "real-time tactical" I got some wikipedia pages and some lists of games in the category from different gaming sites and individuals. Looked like a total of maybe 15 games various people consider to be RTTs, with the total War series accounting for about a third of them.