Nick here from Shopify.
Based on your question (ex. mysite.com/store) I'm thinking a URL redirect could be what you're looking for. A URL redirect will enable you to apply a /store essentially editing the URL structure and customising it you what you'd like.
You can see the URL redirect from Online Store > Navigation > URL redirect Shopify has a helpful guide going into this in more detaila also which you can see from here.
Hopefully this help and is what you're looking for. Don't hesiate to ask any other questions about anything.
All the best, Nick
No. You'd need to opt for the subdomain method instead of the subfolder.
I have the same question "can shopify be setup on a subdirectory/subfolder" and came across your response while searching the community forum. You're clearly a Shopify Expert so no questions asked there, but would really appreciate understanding further why it has to be a subdomain (and not subdirectory/subfolder).
Does it have anything to do with the existing domain and being able to only have one A record associated with the primary domain (thus not being able to point it to Shopify if its already being pointed at the existing self hosted wordpress site)?