@CosmicCat1543 The system that allows him to reincarnate is the same system that holds all the skills he takes on, and could theoretically generate those skills without the people he takes them from having ever existed. Likewise, the system itself must exist through time as well.
Each time he dies he comes back to life having 'suddenly gained all those skills' from an outside perspective, which does check out from either an outside perspective or the reality of it, given everyone that gets skills in this system is indeed randomly given it, it seems, and again, internally it checks out given the system itself is the one administering him dying and coming back. It works whether it's timelines or loops, really, since yeah, it could just as easily be the system giving him a new skill regardless.
Likewise the kill counter is generated by the same system, so it also tracking between worlds or between loops regardless makes sense.
Is the system itself a omnipotent plot device? Well yeah, but I don't think anything is particular wrong within that framework so far, it's logical that it's not constrained by things it allows someone else to not be constrained by.