Up to the point where he refers to "Edit> Copy merged (Shift-Ctrl-C) and pasted this to a new layer:" you can do it exactly the same way (even the menu paths are the same, I think). For that bit, create a new blank layer on top of your others, ensure that layer is active, then hold down Alt (or Option on the Mac) and select Merge Visible. There isn't a specific "Automatic small scratch removal" tool, but if you feel your photograph needs something else at that point then you could play around with some of the
PS filters and see what you can achieve.
Don't forget the other options for color cast removal in
PS -- the automatic or semi-automatic options include Auto Color, Variations, or using the grey point dropper in Levels or Curves.
And if you have a particularly tricky photo, you can always post it under Help Requested and get some specific advice -- there are many, many different ways to fix color and someone is bound to suggest one that's well suited to that particular image!