The Gardiners of Narragansett, like many family genealogies doesn't actually cite any primary/original sources, and ideally it shouldn't be used as the only source.
Having said that, the source does clearly state that the current profile for Job Gardiner is combining information from two different men with the same name.
The Job Gardiner, born 23 July 1723 is the son of Nathaniel Gardiner and his wife Mary (p. 11) and that Job Gardiner married Anne Fry on 6 December 1747 (see no. 89 on p. 35-36)
It is Job Gardiner the son of Benjamin Gardiner and his wife Mary Howland who was born in 1731, died 1800 who married first Hannah Britton, and secondly an unknown woman. (see bottom of p. 34)