Interestingly I had no idea the rules would support this. I knew the part of it being rules text, but I never noticed a similar card without that phrase so I always thought that was the reason.. The more you know
It's always something to keep an eye out for: If it isn't in reminder text, it isn't actually implicit in the comprehensive rules. That's also why reminder text gets to be a bit looser (The land continues to burn.)
Something I feel like pointing out is there are very good reasons Wizards of the Coast specifically does not utilize that rule when designing cost reduction effects. That rule and the handful that follow are there mostly there to clarify "what if" scenarios. "It works within the comprehensive rules" is not the same thing as "It's good design that you should actually use."
Nith, the Pain Sharer ::B::::R:: Legendary Creature - Azra Warlock ::uncommon:: Haste, first strike At the beginning of your end step, if two or more players lost life this turn, draw a card. 2/2
In 1v1 your archetype would include paying life, as you can only trigger the ability if both you and the opponent lose life. But this gets better in a battlebond or commander game as you have multiple opponents to trigger the ability instead.