Potential PhD supervisor expressed interest, then didn't follow up about meeting. Should I continue with admissions process or move on?
Don't panic.  The fact that you haven't heard back from him shouldn't be interpreted as a sign that he has lost interest in working with you.  It's summer, and academics often take vacations or travel to conferences in the summer.  It often happens that they take much longer to reply to emails.

Go ahead with anything that you already know you have to do, such as submitting the online application.  It doesn't sound like any urgent action is needed from the professor - you just want to chat with him about research when he has time - so just wait for him to respond.  If you don't hear anything within another week, send another email.