For your example, the Venn diagram is a good visualization of the filter being applied. Its sets are the values that are being filtered over. I.e., the left circle contains the values {1, 2, 3, 4, 5}, and the right circle contains the values {1, 2}. No, this doesn't explain the entire join operation, but that wasn't ever the goal.

The diagrams that the author of the article comes up with (with the exception of the cross join) are just Venn diagrams rotated 90 degrees.