I opened the QR code with a QR reader, because when I say the app-store buttons, I assumed the QR code was for downloading the app.

You could:

1) Have the QR code contain a real URL, with the Expo ID appended as a querystring.

3) On the server, redirect to the appropriate app-store depending on the browser used to open the URL, or open sketch if installed.

3) Have Expo interpret the querystring to open the correct "sketch".