Is TSP a more detailed form of the "Set Inclusion" question?
As far as I can see, your model is that the edges of the graph are represented by cards and the edges on the optimal TSP tour are cards with blue backs. You're asking if TSP corresponds to the problem of identifying the cards with the blue backs.  If that is the case, the answer is "yes".

However, there is a huge caveat. In the set inclusion problem, we can tell in constant time if the back of a card is blue: you just turn over that one card and look at it. You assume that we can do the same in TSP: in constant time, we can tell whether any single edge is in the optimal tour. This is a completely unrealistic assumption because it's impossible to tell if an edge is on the optimal tour without examining at least one edge from every vertex.

I think that what you've observed is basically that, if somebody has somehow solved a TSP instance, you can find the solution by asking them whether each individual edge is in the optimal tour. This is obviously true, but it's not very interesting.