If you have any questions regarding the Theme X Responsive, please write it here (or create a new topic).

2015-06-21 - 1.2
- Larger Images (400x400) on product page, now responsive and optimized together with the Product Zoom Widget

2015-06-16 - 1.1
- Fixed bug with color-squares

2015-05-27 - 1.0
- Initial release

Is it enough to use the archived theme folder in order to use the theme?

Yes, everything is in the zip file.

So, I tried to just use it but nothing is working. Do I need to set up something additional?

Please explane "nothing is working". No, you don't need to set up something additional.
Have you unblocked the zip file before extracting?
http://blogs.msdn.com/b/delay/p/unblockingdownloadedfile.aspx

I did the unblock but without any success.
You can see what I mean here:
http://188.254.178.43:91/

Any chance to run it with a domain (not ip) and standard port 80 (not 91)?

I have 4 other themes on this site and they are working fine.
I can try to upload it on a hosting.

It is working with no sliders on my hosting. But what is the difference?

here is a site. But I think it is still not working properly : http://www.ga6teta.net/