Is the age to buy alcohol in the duty-free in an airport the same as the country?

The laws on alcohol purchase in an airport are set by the country the airport is in, and are almost always the same as purchasing outside the airport. I haven't researched the specific case of Malta, but I would expect you would be OK.

Note that countries also have laws about how old you need to be to import alcohol. In your case you will be OK, as the minimum age for a duty-free alcohol allowance coming to the UK is 17.