From a legal point of view the pedestrian route there certainly exists, and it is physically possible for it to be used, despite there not being a dedicated physical path occupying that section.

These three aspects are all important, and can/should be recorded in OSM. This can't be done without the way being present to hold the tags (designation=public_footpath + foot=designated + highway=no). Without the way, we would not have this information, and there would be no way to tell whether the route exists or not or is accessible or not on the ground. i.e. it would not distinguish between the route not existing there and that part just not having been surveyed.