What is the purpose of Vih and Vil in the comparator's datasheet?
It's for the logic inputs: SHDN - shutdown; and LEA - Latch-Enable Input - 

When SHDN is high, the MAX961/MAX963/MAX964/MAX997 is shut down.

The MAX961/MAX963 include internal latches (ie the LEA) that allow storage of comparison results.

The MAX999 doesn't have any of these logic inputs.