Artscroll's note there says they follow the tradition that psalm 93 directly continues psalm 92, which they interpret as being about the messiah - in the future.
Rashi says: יאמרו לעתיד
I forwarded your query to a friend at Artscroll, and this is the response I received: "The Hebrew words are in past tense. The suggested translation, while graceful, has the word 'lavesh' once in past and once in present tense. Ours follows Rashi, Radak and Metzudos, who say that this declaration will be made in Messianic times." Hope this helps.
In his commentary, Rashi explains that Hashem reigning refers to the future.
The previous Chapter 92, "to the Sabbath Day" was interpreted by the sages as referring to the future Sabbath of the redemption. Thus recognizing Hashem's infallibility, Chapter 93 is the next step in which Hashem's kingship will be recognized by the nations, or coronated, if you will. Radak states that from this chapter until Chapter 101 are all referring to the future days of the messiah. This includes most of the verses recited in the Kabbalat Shabbat service established by the Kabbalists.
Artscroll's translation, here and elsewhere, is based on Rashi, who notes in his comment on Ps 93:1: ה' מלך - יאמרו לעתיד, i.e. that this Psalm is going to be said in the future.
I looked up the Nishmas Chaim, I don't see him mentioning that this story is cited in Sefer Chassidim. Anyways, I was not able to find it in the standard edition of Sefer Chassidim, I don't think it's in the Mekizei Nirdamim edition either. The source for this story, by the way, is Tractate Kallah 6:1.
The Artscroll Siddur (Siddur Kol Yaakov, Mesorah Publications, 1984) contains an unusual translation of the first verses of Psalm 93. A more conventional translation might be: