The ebuild uses python-any-r1. As a result, qvim links to a random Python implementation installed and lacks proper dependency on it. The build should use python-single-r1 instead, much like vim and gvim.
Please feel free to fix this. I really need to take another look at the ebuild, especially since the new vim ebuilds have dropped the old eclass. But I don't know when I'll have time for that.
+ 16 Oct 2013; Michał Górny <mgorny@gentoo.org> +vim-qt-20130201-r1.ebuild, + +vim-qt-20130220-r1.ebuild, -vim-qt-20130201.ebuild, -vim-qt-20130220.ebuild: + Fix Python support, use python-single-r1 since the package links to a specific + version of Python.