Judging from this, it more then likely is the formers portions of the race course.
From the Hoylake Website:
The Hoylake links can be, by turns, beautiful, uplifting, awe inspiring and, on occasion, soul-destroying. They were created to be a demanding test of golf and remain so, and they lie at the very heart of the history and development of golf in Great Britain.
Built in 1869, on what was then the racecourse of the Liverpool Hunt Club, Hoylake is the oldest of all the English seaside courses with the exception of Westward Ho! in Devon, which was established just a few years earlier. Robert Chambers and George Morris were commissioned to lay out the original Hoylake course, which was extended to 18 holes in 1871. This was also the year in which the Club was granted its Royal designation thanks to the patronage of His Royal Highness The Duke of Connaught.
For the first seven years of its life the land still performed its original function, doubling as a golf course and a horse racing track – indeed, echoes of this heritage can be found today in the names of the first and eighteenth holes, Course and Stand, while the original saddling bell still hangs in the club house. Once the horses had been dispatched to pastures new Hoylake began to take its place in the history of golf in general and of the amateur game in particular.