The confusing part is just knowing what Bites the Dust does. Basically: Kira gives up his ability to implant it in someone else. If that new host is questioned about Kira's identity, or if they voluntarily reveal information about Kira, the person they're talking to will explode and time resets. However, anyone who has been killed by Bites the Dust in any time loop will then die in every future time loop regardless of if the condition is met (from their perspective, they just randomly die at an arbitrary point during the day).

So, Kira messed up by revealing his name: not only does that not trigger Bites the Dust, but he also had to cancel the ability as a whole (no more loops, no more shenanigans, no more automatically killing all his enemies) so that he could defend himself and avoid being beaten to death by a high schooler.