I couldn't make out the name of the road he lived in the 'Walton-on-the-Hill district, but a couple of people on facebook said it was it is Wylva Road, which is near the Anfield Stadium and where the team played in 1891 before the move the next year. Sadly, one pointed out that Dick Molyneux lies in an unmarked grave in Kirkdale Cemetery.
The census shows he was born in St Helens (Wikipedia wrongly states Prescot, but that was the birth registration district for the area), and here's the 1861 Census showing him living as a three year old in the Parr district of Blackbrook, St Helens, probably near to the Ship Inn. His father Thomas was an 'Underlooker' for a colliery which meant he deputised for the operations and safety of the mine.
A fascinating bit of history, with echoes for these current changing times for the 'Grand Old Lady' Goodison Park stadium and the football club. Take a read of the great article by the Eveton FC Heritage Society too.