How to stay in touch with professor after graduating?
As far as my experience goes, this 'we should stay in touch' with no concrete suggestion as to how you should stay in touch, means he does not expect you to actually stay in touch on an ongoing fashion. 

The way I interpret the meaning of this phrase as it appears in the email you quoted, it means roughly the following: "I am a busy man, and I have no particular thing in mind that we should cooperate about at the moment. But I like you, I am thankful for your comments, and I am impressed with what you achieved so far and by your potential. So if at any point in the future you see a concrete way in which our relationship can be put to use please contact me, and I will do the same on my side."

So I would just answer back saying something like "I'm glad were helpful. I'd be happy to chat more if you ever want [more comments about the current paper or anything related to the it or the job that you are doing now]."