Yeah, this is sometimes really interesting. For eg Scotland, Wales, NI and England are technically all different countries. Just like Aruba (and other Carribbean/island micro nations) which technically is still in the Kingdom of the Netherlands.
Games like EU4 do have multiple views of the map for this reason. There are so many ways you can subdivide and draw borders differently. Language, culture, religion, imperial, etc.
Westphalia did two big things in my view… 1. is permanent diplomacy and 2. it made sure that things were on a secular not papal foundation. It’s a big deal but to claim that countries weren’t a thing before it is a bit of an overstatement.