That confirms other information, i.e. that Jane had died and Joseph was still alive.
I see that Joseph is described in the 1871 census as a widower, aged 62, born Aberdeen Old Machar.
There is no death of a Margaret Watson, other surname Carruthers, in the deaths index at SP. So did Margaret leave Joseph and go back to Ireland with their son? Did she die in Ireland between 1861 and 1871?
There are six Joseph Watsons born 1808 plus or minus five years in the deaths index on SP:
Age 61, died 1873, Edinburgh Canongate (YoB 1811/1812)
Age 67, died 1876, Dumfries (DoB 1808/1809)
Age 77, died 1882, Paisley
Age 79, died 1882, Dunfermline
Age 78, died 1884, St Martins
Age 77, died 1888, Auchinleck
There are five Joseph Watsons born 1808 plus or minus five years in the 1881 census:
Age 78, Dunfermline, born Renfrewshire
Age 75, Paisley, born Campsie, Stirlingshire
Age 74, St Martins, born Perthshire
Age 71, Lochlee, born Errol
Age 69, Ayr, born Ayrshire
I've coloured the ones who match, leaving just two possibles for your Joseph. The one who died in Edinburgh is a few years too young. Have you looked at the death certificate of the one who died in Dumfries?