It is not essential as the bay and restaurants are all within walking distance. However when it is very hot a car is advisable. If you eat at the local restaurants, they will pick you up from the villa and drop you off.
If you want to explore the Bozburun or Datca peninsula, you can hire a car by the day and have it delivered to the villa.
Check the website for more details. When driving please carry your UK driving license and/or your passport as photo ID should be carried with you at all times when you are in Turkey, and you may be stopped at a police checkpoint and asked for it.