Couple of points on the map, no sign of the Castle pub on it although the Wellington is marked as a PH and St Albans Terrace instead of road. Have I missed something because some of the family had a shop in St Albans road we always understood.
I've posted another copy of the map showing St Albans Road better - as you can see, in 1911 it hadn't yet been extended to meet Wallasey Road. I've also added maps of the same area from the 1899 Edition OS and the mid-1920s Edition, courtesy of old-maps.co.uk (though oddly on their webside the 1920s map is labelled as being from 1911 - it clearly can't be, as it shows the new Boot Inn which wasn't built until the mid-20s).
As for the Castle not being labelled as a PH, that was often down to the whim of whoever draughted the map, and also whether there was room to fit the letters in anywhere! Plenty of other pubs and beerhouses were never marked as such on OS maps.