Your map, on your own website
Your map doesn't have to live only at its own address. There are now two ways to put it on your own website.
Embed it
Paste one line of HTML into any page and your map appears inside it, just as the apps do on mapifest.app. It behaves like part of your page and leaves your visitors' Back button alone. The F.A.Q. has the line to copy.
Or host it yourself
Mapifest takes care of hosting, updates, messages and statistics. But your content is yours, and you can take it with you: export your app, with its photos, audio and the map area you choose, and host it on your own website, at an https address you pick before exporting. In the editor, it's the Hosting card on the App tab.
An export is a snapshot. When you change something, export again.