Yes, if it doesn't say that they are births or whatever, you should key them as "other".
William is the father. John is the grandfather, but you don't need to key his name. Prudence Isle is the name of a place on Rhode Island, not a person. (I had the same confusion the first time I came across Rehoboth!) It's not very clear whether Mary is the mother or the grandmother because there is no comma between John and Mary but I think she is probably the mother.