A fire stick actually does not need a smart TV.
It requires a TV with an HDMI port.
However, what you need for the Firestick is good Wi-Fi. Preferably constant high speed would be preferred. From my experience, the only Wi-Fi offered at Royal Islander, is quite slow and may not work your Firestick due to its lack of speed and intermittency.

I own a property across the street in the sister building and I have my own Wi-Fi, which is significantly faster and it does run either a smart TV, or a Firestick plugged into a TV with an HDMI port.

Perhaps someone has tried it at La plage.

Drphilsxm