I think he's trying to say he should be doing Piercing damage with his small longsword, because it's close to a shortsword.
I don't think it would be, because a dogslicer and a shortsword are the same size already and fairly similar but one does slashing and one does piercing.
Changing the size of a weapon doesn't change its damage type.
And taking a size penalty doesn't let you treat a properly sized weapon as a different weapon of a different size.