It surprises me that the footpath is the responsibility of the railway at all tbh, apart from linking to the railway station at one end it doesn't really have anything to do with the railway, you'd have thought it was more naturally the responsibility of the local council.
Given how it has been closed, presumably it isn't listed as a public footpath. The lack of a mention of that in the news item suggests the same. I suspect the land belongs to the racecourse, and it is made available, or leased, to the railway for race day crowd handling.