Mary is not his daughter but is claimed to be a descendant. Her estimated date of birth is around 1785 (based on her granddaughter's dob being 1834.
According to Family Search IGI, a John Houston who married Margaret Shaw about 1650 was born about 1630. They had a son John Samuel Houston born 1664 who married Margaret McClug in 1685 in Ulster. This fits with our data but I have not added John Samuel and spouse at this stage since he is not a brother of Mary and the info would be confusing. And we don't know if he is in Mary's pedigree.,,