The MiniPro which you have will read 2716 Eproms but cannot program the majority of them due to the requirement for 24-25 Volt DC to write to them.
You can use a 28c16 Flash device as a direct replacement for a 2716 and the minipro programs them fine.
The MiniPro is a very good apart from 2716 programming, its built in logic and ram test are very useful.