Welcome Brausoft!
Oooohhh, that's too bad, because there is an Inkscape extension for drawing jigsaw puzzles, and they are like the traditional kind of pieces (afaik). Speaking of the pieces though, can you give us any more guidance about how the pieces should be shaped? "Not like traditional jigsaw pieces", and curved rather than angular, still covers a lot of ground!
I'm not clear. Are you asking if someone would be interested in doing the work for you? Or are you asking how to do it?
Depending on how that jigsaw extension is made, it might not be very hard to program new shapes. I think I'll try to contact the author, and ask if different pieces can be used. I would love to make an abstract, really hard jigsaw puzzle!
Do you already know how to make the game? What kind of file (or objects) do you need to input?
Depending on how that app works, I suppose you might need to either draw the cutting paths by hand, using Pen/Bezier tool, or use Clipping. (Help menu > Inkscape manual > Clipping) I've actually done this before, (testing out a new Inkscape extension that produces animated HTML5 docs (below)). I used clipping for that. And then I had to save a bitmap copy for each clipped piece.
If you can tell us what you need, to send to the game making program, we can help you do it.
XIA
http://xia.dane.ac-versailles.fr/index_en.html. This is a whole different extension than the jigsaw extension.
And this is the link for the jigsaw extension. Oh, I see it's for laser cutting. I'm not sure if you would be able to get what you need from that extension, without sending to a laser cutter. Maybe though.....probably, I'd say.