Islands can have EEZ's but I strongly doubt Egypt and Greece's claims will be upheld due to precedent.
The International maritime law on delimitation of continental shelf and EEZ states that the EEZ needs to be proportional to the length of the respective shoreline.
https://www.un.org/Depts/los/nippon..._pages/fellows_papers/dundua_0607_georgia.pdf
What Egypt and Greece are trying to do here is similar to what France attempted to do in 1983 with Canada in relation to the St. Pierre and Miquelon islands which are located about 20 km offshore from our country. France basically stated that they get 200 nautical miles of offshore EEZ from the Islands and it went to the International Court of Arbitration with a judgment rendered in 1992 declaring France was only to be awarded 24 nautical miles of EEZ which wound up making the islands EEZ's completely embedded inside Canada's own EEZ.
https://www.heritage.nf.ca/articles/exploration/france-canada-boundary.php
The same thing happened with the Channel Islands owned by the UK whose EEZ was dropped to 12 nautical miles making it embedded within France's own EEZ.
Kastellorizo is significantly smaller than St. Pierre and Miquelon islands as well as the Channel Islands. I hardly doubt it would get almost anything let alone what Greece and Egypt are trying to claim.
Turkey's deal with Libya and its claims will stand.