Saved (starred) places in Google Maps live under your personal account, not as a shareable link, which is exactly why there's no direct export-to-GPX button for them. Google Takeout technically exports saved places, but only as a CSV of names and addresses, zero coordinates, so it isn't usable on a GPS device without a separate geocoding step first.
The fix takes about a minute: in Google Maps, create a new list, add your starred places into it (tap a saved place, then "Add to list"), and use that list's Share option to generate a public link. That link is what MapsLinkQuest reads.
Paste the share link into the converter above and download a GPX file with the real coordinates for every place, ready for Garmin, Gaia GPS, OnX, or any other GPS app. No Takeout export, no manual geocoding, no premium anything.