I thought it was perfectly clear when I saw it
Rule Clarification for Multiple Checks

I thought it was pretty clear because it said 'triple-checks' afterward. But I agree that it could be confusing at a glance, so it might be good to change the wording.

Reading the rule, I thought the bonus was awarded to a player checking a king already in check by another player. Hence the possibility to double or triple check.

I agree. An interesting fact: in Chinese chess (Xiangqi) quadruple checks are possible, although rare. Triple checks are more common.

I got confused too until someone did a double-check when I was playing. After that, I got confused for a second and got over it.

The part that confused me was that only checks by the piece that moved and discovered checks (even if the attacker is by an enemy piece) is what counts.

To clarify what I mean:
[...] Double and triple checks must be made in 1 move. If a player moves a piece that allows a discovered attack on another player's king and at the same time checks another king (be it by discovery or standard check), that is a double check (even if it wasn't his piece). The same applies for triple checks
https://www.chess.com/clubs/forum/view/double-check-against-player-that-resigned-timeout
The rules related to multiple checks should be clarified... I mistakenly thought a "standard" double check (i.e. a move causing multiple pieces to simultaneously attack one king) would be awarded with points. Was anyone else confused by this?
Rule should instead be worded "A move placing 2 opponents in check simultaneously will be awarded +5, and 3 opponents simultaneously will be awarded +15" or something to that effect.