I had a look at the Attestation papers you mention and wonder if they are the correct ones. There is another set of papers on Ancestry with different soldier numbers that actually give Samuel and Mary at Harrison Street as next of kin. Also mentions brothers David and John.
Samuel appears to have joined up initially on 21/5/1912 (giving a false age). He joined the Royal Irish Fusiliers ( number 2959). He served with them till 20/10/1913 and immediately thereafter transferred to the Royal Enniskillen Fusiliers as soldier number 10/570 ( but stating previous service under number 2959). On this document he gives his parents at Harrison street as next of kin. He served until 15th May 1914 when he was discharged due to having given a false age when he first joined up.
There is also a comprehensive tree for this family on Ancestry. It has some issues - for instance it gives marriage and subsequent history for Robert James, including a death date. However further checks on the supposed marriage indicate that this Robert was actually the son of a Robert Boyd so the tree owner has made an error somewhere. The tree indicates that Samuel Snr died in Belfast in 1925 and Mary died in 1941. I suspect the tree owner is a descendent of the Robert James, but it may be that having linked him to the wrong family he then obtained correct info for the erroneous family. You would need to check this out.
