They are just timers that can be used for any purpose anyone can think of for keeping track of time in a system. Just like any other timer.
The timers can be set to elapse after a certain period of counts, and the status of both timers being elapsed or not can be read from the OPL chip status register.
In addition to just reading the status, the timers can ...
The Yamaha Applications Manual (not the Data Sheet) describes how to use the timers and IRQ output.
See https://usermanual.wiki/Document/Yamaha20YM381220Application20Manual.26216546/html Sections 3.1.2 and 3.5.
Even if the chip signal pins were not connected, one use for the timers was to check if the computer had the chip installed.
This Programming Guide ...