I see. That's a pretty solid way to keep your elementals from becoming overpowered.
It also makes what they do more akin to how magical powers are described in ancient myth and folklore rather than how most modern fantasy fiction depicts them. Which I'm under the impression is the vibe you're going for.
Ehhh, it's uncertain, to be honest. We've often debated exactly how telekinetic type magic (moving stuff with your mind) should work in Wulfgard. We generally avoid using it.
The current rule is that it's very hard for magic to directly manipulate living beings or anything else that possesses a spirit or soul (which includes people, animals, and even things like oceans, rivers, forests, etc.). Only very experienced and powerful mages with strong spiritual presence themselves can overcome the natural protection to arcane manipulation provided by a spirit. Usually if they want to manipulate these things, they have to resort to spirit magic.
So, typically a mage who wants to "force-push" a living being will just summon a strong gust of wind (air magic) to knock them down. But it's far beyond the realm of air magic to form some kind of tight constriction around a person's throat.
The rule I used in the Errant RP that I ran was that a very powerful mage with a very strong spirit can use "force magic" directly on a living being if the target's spirit is not powerful enough to stop it, but that's not a set-in-stone Wulfgard rule.
How about using 'air magic' to pull the breath out of someone's lungs, and keep other air from going in? That would have essentially the same effect as choking them. Or do the mages just summon an element, without having direct control over it?