Yes, it's the old raid ID system. It's understandable that it might confuse folks used to the more flexible loot-locked system we have in Normal/Heroic - with those raids, if you leave after three bosses into a raid, you can come back on a fresh clear and kill stuff until you get to a boss you haven't looted yet and start getting loot again. With Mythic, you and everyone in the raid who kills the first boss are bound by the raid ID - the 20 players who killed that boss are basically in the exact same instance of said raid, and if two people step out on boss 6 and are replaced, and the raid continues on to kill all the bosses, that's their raid ID - if they formed a raid and zoned in after the clear, they would arrive in a cleared out instance.
It's clearly all part of the design to keep Mythic as something more akin to the old days of raiding, where server communities formed and fought for realm firsts. I admit, it's not a raid ID system that appeals to me anymore, but it's not complicated - it's the raid ID system that we've always had.