The license does allow for it, but it's actually sort of tricky to do if you want to import it into a non-mediawiki system. Wikipedia makes really extensive use of templates in wikitext, which can be complicated nested things that can call out to Lua modules.
You can easily take Wikipedia's HTML output and use it, but reusing the source of those articles requires a lot of work on either compatibility or translation.
If I were attempting to create a less "captured" Wikipedia alternative that's what I would do - start from there and try to keep it synchronized while hacking at it slowly, instead of taking a from-scratch approach.
There have been many Wikipedia forks, but all have failed, because 99% of the work is in doing uncontroversial stuff that most people are fine with, and 1% is in controversial "captured" areas. If you fork the whole thing in the hope that you can fix the 1%, you will have to find a way to do the 99% bit.
You can easily take Wikipedia's HTML output and use it, but reusing the source of those articles requires a lot of work on either compatibility or translation.