By definition (or perhaps convention), if we say a router is setup as an AP, we mean it's NOT providing internet access. So I’m assuming you actually have this router/AP connected to another router, the one actually providing internet access.
[primary router](lan)<-- wire -->(lan)[router - ap only]
What’s probably happening is that when the guest SSID is enabled, it's only routed to the WAN on that same router. But of course, you're not using the WAN on that router. You have it configured as only an AP! (at least I assume you're not using the WAN, but have them connected LAN to LAN).
And if you think about it, it makes sense. The point of the guest SSID is to keep those users separated from the rest of your network. So rather than bridging those guests to your LAN or primary SSID (which would make the internet available), they're keep isolated and only bound to the WAN (internet). But again, that's a problem as you've configured your network since the WAN is not in use on that router (now configured as an AP).