Will minecraft work on MacBook Air 13?

Yes Minecraft works fine on a Macbook Air. They are probably giving it to you for free because it is loaded with malware (both Minecraft and the malware use the Java programming language which is notoriously insecure) that can cause you and your computer a lot of problems and so is probably not worth it.

http://www.pcworld.com/...-soon.html

http://www.oracle.com/...72971.html