/usr/bin/wmii shell script uses xdpyinfo for something. Without xdpyinfo, wmii refuses to start.
And while using a modular X, xsetroot and xmessage should be in the list of dependencies, too.
14 Jul 2006; Torsten Veller <tove@gentoo.org> wmii-2.ebuild: Added x11-apps/xdpyinfo to RDEPEND. Reported by Michael P. in bug #138756.