I think it's important to clarify context. As suggested in comments, the linked article refers to tap-targets on mobile/touch devices...
roughly 7mm, or 48 CSS pixels on a site with a properly-set mobile viewport.
"48 CSS pixels ... with a properly-set mobile viewport" does not necessarily mean 48 literal screen pixels, since a "CSS pixel" is relative to the viewport. The easy to measure physical metric here is roughly 7mm.
If tap-targets are considered too small then your mobile-experience rating is going to be lower and Google might not give you the "Mobile-friendly" badge in the mobile SERPs. Mobile "friendliness" is supposedly a metric that Google now uses as a ranking factor in mobile SERPs (one of many), but it could also affect click-through rates if you don't have the visible "mobile-friendly" badge.
So, yes button size can affect mobile SEO. How much it affects SEO is another matter.
https://developers.google.com/speed/pagespeed/insights/That guild is to improve this google page speed score. Here you will also get score of user experience.