Two things: elsewhere and in earlier Geni versions he is described as the 4th Earl of Lennox, which makes sense to me because his father was the 3rd Earl of Lennox. So...why and how did he become the "13th"?
Also, I don't claim to be an expert so perhaps I'm mistaken, but Stuart and Stewart although related are not precisely the same family. They're not really interchangible that I'm aware of. I was under the impression that Stuart was the older, "royal" form (or vice-versa, it confuses me too). Also again, elsewhere and in earlier versions his surname was spelled "Stewart" -- matching that of his father. So...why the change?
Cawley has it spelled both ways, depending on where you look. He seems (imho) as confused as most people are by the two different spellings.
http://fmg.ac/Projects/MedLands/SCOTTISH%20NOBILITY.htm#Matthew13Le...
http://fmg.ac/Projects/MedLands/SCOTTISH%20NOBILITY%20LATER.htm#_To...
Also I can see that it is given both ways on Geni, so the Display name doesn't exactly match the file name. Imho the display name is way out of whack.
But on Pedigree IV of "The Heraldry of the Stewarts", Stewarts of Bonkyll (part one) -- he is I believe correctly identified as Matthew Stewart, 4th Earl of Lennox.
https://digital.nls.uk/histories-of-scottish-families/archive/95587...
I uploaded a pdf copy of the pedigree for our subject, generated by the National Library of Scotland, to his profile. Also if you take a look at the two-page List of Illustrations, this book gives very precise and proper spellings of the name for every specific House. This list is on pp.15-16 of the online source.