I bought the library “vintage keys” for my Motif ES Rack.
Now I dumped some sounds to my host (Logic) and tried to dub them to my new S70XS. It did not work. Thank you for help!

Yeah, that will not work. The Motif-series and S-series are different product lines and the ES and XS are different synth engines.

There is some VOICE compatibility between products but the gap between the ES and XS is a huge one… entirely different Effect processing is used in these engines. So even if the Voice’s Waveforms (or a substitute) was found, it is likely to sound very different in the other product. So much so, there are different versions of the library made for the XS units.

Thank you for your answer.
If I buy the soundset again, is it compatible to my S70XS?
http://shop.motifator.com/index.php/vintage-keys-voice-bank-for-yamaha-motif-mo-x.html

No, the data for the MOX cannot be read by the S70 XS

But if you purchase the data for the Motif XS you can IMPORT it into the S70 XS using the S90 XS/S70 XS EDITOR (The Motif XS data will work because it provides a .X0A file which can be read by the S70 XS)
http://shop.motifator.com/index.php/voice-libraries/motif-xs-voice-libraries/vintage-keys-xs.html

Please notice the important difference between your LINK (for the MOX) and the one I provided (for the Motif XS)

It makes a difference! The S70 XS cannot read MOX data (period). It can read Motif XS Voice data!