I see the same thing! My waypoints are showing on the initial/staring mobile view (Android) but not the route. When I switch to desktop, then the route appears but it's clunky and the initial sidebar blocks the map which creates a second confusing set of instructions for viewers.
Add one more to the list for tripping on this issue. My shared course clearly shows on the desktop version of MapShare, but my mobile phone (android) defaults to a mobile version of MapShare and does not show the course. If I force it to switch to the desktop version, the course is there.
in Chrome and Firefox ... On my Android ... both mobile and desktop mode is not showing my tracks... I have not tried to show routes .. like its only currently showing a blue dot on current location... but in Desktop I can see the collection of tracks that I have shared .. properly .. I cannot reconcile this even using desktop mode on multiple devices.
In the left sidebar, be sure that the eyeball icon on the row with your user ID is NOT slashed. If it is, click it. This is probably not the problem if you can see the triangular blue "head pointer".
On the map itself, look for the triangular head pointer. Attached to it, you will see a small white circle with a + or - in it. If it currently shows plus, click it to show the tracks.