The space has history dating back to the very original arrival of the British because it was the site of Possession Point - where a flag raising ceremony took place and formal possession was taken of HK Island. It's an historical event still marked by the name of Possession Street an adjacent thoroughfare that connects Hollywood Road with Queen's Road. Before it became the park the area was a Tai Tat Dei (Chinese: 大笪地) a sort of open market place where hawkers sold all kinds of stuff and often called a "poor man's nightclub".
At the moment I'm not aware of the layout of the place but if you follow the link (supplied by Thomas): https://sc-whybother.blogspot.hk/2014/03/blog-post_8.html and scroll to the bottom, you'll see some old pictures of the area (as well as a screen grab from this very same film). It looked like there was two circular concrete kiosks and a few single-storey concrete huts. A closer look at the layout (and perhaps better placing these grabs) will have to wait until I can find some more helpful pictures.