That is strange but not completely unheard of.
There are a couple of Aussie cricketers I know of (Shane Watson and Jason Berendorf) that bowl with 1 arm/hand and write with the other. There is a current England cricketer (Jack Leach) who bowls left arm but throws right arm. You'd have thought he should try and develop his skill set to be ambidextrous like the guy @cryptoandcoffee is describing.
In cricket there is a theory that you shouldn't class a batsman as right or left handed. Instead you should refer to them as top or bottom hand dominant. I don’t play golf but I suspect you could make a similar argument.
In Ireland that grip is called the Hurly grip and it is the plagued of Irish golfers as we all use the hurley grip starting in golf only to reach a certain handicap. It is rare that the hurley grip succeeds in the low handicaps . I see one pro with the hurley grip on the PGA and he is some journeyman. I changed my grip and I regret not staying with the hurley grip as I was bloody better. Now I'm shit