It seems to be clamped to the cylinder head, like the examples Joe mentioned - that looks like an original equipment retaining bracket to me. At least the hose is restrained so it can't flop around. If the hose has not gone hard where it is hottest (around the retaining bracket) over the last 21 years since 1988, it sounds like it will be OK unless you eventually find you have vapour lock problems on days when it's way too hot to mow grass anyway.
