Third feature request, a "without tags" filter, identical to "with tags" filter.
UI components allowing clicking on a tag (e.g. the existing game detail view)
would simply toggle between "unselected" (slightly grey as current behavior)
"with tags" (again, as current behavior) and "without tags"
(red, triggered by clicking an already selected tag present in the "with tags" list)
Suggested by Dragonfyre13 via Chat