Not necessarily. To suggest that souvenirs are only used for showing off is pretty cynical. For example, I cannot fathom how people buying fridge magnets use them to let everybody know about their trip. I doubt they buy them with the intention of signaling to their house guests every time the guests look at their fridge. A lot of people buy souvenirs (memorabilia) just for themselves because they evoke nice memories.

If the goal was to let everybody know that you went travelling, you can simply post pictures in some social media network.

That's precisely the argument he was making...

Buying impractical things for social signalling is not characteristic of frugality.