While these are also commonly referred to as "invocation artifacts", they aren't actually artifacts. This also means they don't affect artifact wishing negatively as they don't increment the artifact count.
Artifacts are not unique items in the sense of this article. Instead, their base item is a normal type of item, except the artifact has a special name and additional benefits. For example, the Eye of the Aethiopica is a named amulet of ESP that also provides faster energy regeneration amongst other extra powers.
Stormbringer and the Tsurugi of Muramasa are the only runesword and tsurugi, respectively, that can not normally be generated in the game, but neither count as unique items. It is, however, possible to find a non-artifact runesword or tsurugi in a bones file (if the artifact has already been created), or by wishing for one.