"Thank you for reporting this. That said this is a known issue to us and it is currently being worked on. Furthermore, it should be fixed in the upcoming patch. That said, at this time, I am afraid I am unable to give you an estimated time of a release of that patch.
Sorry for the inconvenience and thank you for your patience."
(c)
GOG stuff

So, game launched week ago and no any progress with fixing simple (but critical important) element.
I will refund game and just throw away this problem from my head.
Good luck, people, with this piece of... game development.

Good news! :)
The game has just been patched (the patch is available on Galaxy but not yet as a standalone patch).
The mouse cursor is finally working properly (it is shown on main menu and map screen, and nowhere else where it shouldn't been seen).
It seems some other fixes have been applied (I have noticed faster load times and tagging enemies now seems to work a bit better) but we should wait for a changelog to know what's been fixed or changed.

They fixed it in the patch released today!

Fixed for me too :) How are people finding the mouse sensitivity in this game? For me it's too low even when maxed out in the options. Anyone know of a way to edit/mod the values?

Yep, it's fixed now. :)