On the very page you link, there is a section called " Map Types " (in the Utils section).
If you go there you will see an example of how you can add a new button (in your case pointing to a map of the same location but OpenStreetMaps):
map.addMapType("osm", {
getTileUrl: function(coord, zoom) {
return "https://a.tile.openstreetmap.org/" + zoom + "/" + coord.x + "/" + coord.y + ".png";
},
tileSize: new google.maps.Size(256, 256),
name: "OpenStreetMap",
maxZoom: 18
});
As explained on that page (my translation):
You can define many map types from external map services. [...] You must define a function called getTileUrl
, that returns a URL of the box depending on the coordinates of the map.