The problem is that the pedestrian part of St Enoch Square is mapped as highway=path, area=yes. There's nothing wrong with this, although I might use highway=footway or pedestrian. Most routers are unable to route over areas, although some work around this issue by routing along the edges of the area.

It's somewhat conventional, although, strictly speaking, frowned upon, to add additional footways as ways to ensure sensible routing. In this case perhaps two ways either side of the entrances to the underground down to Howard Street, with links to the entrance to the shopping centre & the two underground entrances and also possibly to the existing St Enoch Square highway=pedestrian. 

As someone who uses Maps.Me to work how much time I have when going for a train, I have no problem "mapping for the router" in this use-case.

Regards,

Jerry aka SK53