I just called the manufacturer:
The product contains various waxes which stick to the laminate and - as you learned - make it darn slippery.
Your everyday wipes will not remove the wax, apart from traces than may be polished off with lots and lots of ellbow grease and patience.
To strip the wax, you will need a "residue remover", the nice lady recommended something from their own line, of course, the emsal Grundreiniger (Layer remover). Use less than the originally recommended dosage to start, perhaps a quarter, just to be safe. Use more if required.
Another alternative we discussed are those "grease removers" based on orange peel. They are often sold as "Kraftreiniger", my personal favourite is the Sonnet Orangen Kraftreiniger (scroll down, here's an amazon link) I would hesitate to use the really strong ones like Oranex or at least dillute them very, very much.
For both, testing them in an inconspicuous spot is a good idea, but if you start with very dilluted cleaner they should be safe, the customer support assured me.
Independent of your product choice I would recommend using microfiber rags and plan for some scrubbing, mechanical action will support the cleaner's chemical reaction. Also, plan to "rinse and repeat", depending on how much product you got on your floor you may have to remove the residue in layers, not in one go.
The most interesting recommendation I got from customer support was to always wipe the entire floor, not to spot-clean. Laninate will always have very small dents and divots where a tiny bit of residue stays behind - a mixture of dust and dirt and cleaner from your wipes, probably. Spot cleaning might leave visible differences between the place of the spill and the rest, not because it affected the syrface, but because it is niw actually cleaner than the rest of your floor.