I've checked the cencus from 1881 to 1911, and the premises at No.59 were occupied by the Owen family during this time. Mr Owen is described as a 'Grocer Shop Keeper' or a 'Provision Dealer'. During that time his wife and children assisted him in the trade. It seems reasonable to assume that this was a corner shop with the family living above the buisness. Most of the neighbours seem to have had some sort of employment in shipbuilding. I've also checked the other corners of Rodney St, and they would appear to be just housing. Unfortunately, the cencus does not normally indicate the use of the premises, only the occupation of the occupants.
From the photo on the Birkenhead Vigilence topic, the house has obviously had an extensive makeover, with the external brickwork being replaced fairly recently. It looks like the front door has shifted to the side of the house, so now it is the only front door in Helena St. Its original position was almost certainly on the corner, judging by the coping stone, thus making this a true corner shop in times past. The old OS maps also show it without a front garden wall, thus giving room to put their wares on display.
In the Birkenhead Vigilence article on Beer Houses, it can be seen that the possibility exsisted for any premises to sell or even brew and sell beer for the payment of a fee and not need to appear on a cencus or OS map.