Hi Ken @ken-s ,
Like Wayne said, you are not in Vertex Select Mode. (You’re in Face or Edge Select Mode.)
I would recommend you also have a look at this: https://cgcookie.com/community/21922-can-t-see-vertices-when-resizing-edge-loops-with-s-x
Just in case you run into that issue, after you’ve switched to Vertex Select Mode. (But it sounds like you’ve already read that.)