Only regular wrench key for wheel mount like this? With the wheel mounting system like on the photos (sorry for poor quality - this is the best my phone can do) - is my only option to dismount a wheel is to use a wrench? Wheels: CUBE RA 0.8 CX. On the left side it seems that there's a visible thread but I'm not sure what is it for. The ride side shows the end of the axle so I guess nothing to do there.
That looks like a thru-axle that has lost its handle. You can see the threaded bit in the first photo where a handle should have been bolted in. This can happen if the retaining bolt vibrates loose during a ride.

Luckily the axle has flats so can be removed with a wrench but you’ll want to track down a new axle for when you need to remove the wheel by hand when out on the road/trail.
It’s probably a 12mm x 142mm rear thru-axle but length will need measuring against the current part along with the seat type (square or conical) , thread pitch and thread length. The frame manufacturer (Cube) might provide you with an exact specification.
This blog discusses the technical differences in depth very well.
EDIT Changed last paragraph because thru-axles are not standardised.