It's an easy mix-up: Google Maps Lists (the collections you build from regular Google Maps, on your phone or the desktop site) and Google My Maps (a separate, more advanced tool for building custom maps with layers, lines, and shapes) sound similar but aren't the same product.
Google Maps Lists are what you get when you save a group of places from regular Google Maps and share them, no separate app, just the Share option in the list menu. There's no built-in export to GPX or KML, which is exactly the gap MapsLinkQuest fills.
Google My Maps (found at mymaps.google.com) is a standalone map-building tool. It supports a real, native KML export, click the three-dot menu on your map and choose Export to KML/KMZ, no third-party tool required.
So the short version: if your places live in a My Maps map, Google already gives you an export button, use it. If they live in a regular Google Maps list (the far more common case for saved trip stops, favorite spots, or a list someone shared with you), that's what MapsLinkQuest converts to GPX or KML.