The library that cfwindow uses, ExtJS, uses local storage to do some of its work. If cookies are disabled, local storage does not work either, which in turn means the library doesn't work.
Coldfusion's built in windows, forms, inputs etc are all terrible. I would recommend moving to a jquery equivalent straight away rather then waste time.
I mostly agree with haxtbh. First of all (and I'm not positive about this) I understand that the ExtJS that CF packages is an older version than what is currently available. That's not surprising seeing as how they packaged an old Lucene (1.4) for Solr collections in CF10 (Lucene v4.? is currently available, I think.)
As far as localStorage not working if cookies are disabled - it is my understanding that the two are separate and do not affect each other. I do know that if one clears one's browser history, that will clear localStorage since localStorage is per domain (erase the domains from history, erase the stored data associated with the erased domains.) But I've never had a problem storing values or objects in localStorage when cookies have been disabled.
Trust. (Just my $0.02 worth.)