Have another look at that lesson about general destination. I think you will find that "para" is used [not por] in the context of "to / towards" a destination.
In the example which you quoted "Mis abuelos .... por" what they are trying to say is that the grandparents have travelled "through or around" various/ several countries. Por is always used to denote this meaning of passing through. "Diferentes" has the meaning of various and several, as well as different. I hope this helps. Saludos. John
You will find that meaning of por in this lesson here.
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