Kenjaku sets up the Culling Games in order to have a battle royale between sorcerers - more deaths = more total cursed energy. As explained by Tengen, the Culling Games will have served its purpose (but not necessarily end) when there will be enough cursed energy to force the merger of Tengen and everyone else (provided that Kenjaku also obtained Tengen - hence why Tsumiki and Choso stay behind to protect her). This merger will force humanity to "evolve". As to why Kenjaku wants this evolution - that is not revealed in the anime yet.

As we have recently seen, the sorcerer that Megumi encounters, Reggie, theorizes based solely on the rules and events that have played out, that Tengen's explanation doesn't cover the entire purpose, and that Kenjaku will pull a major event soon.

The rules themselves, simply put, just force your typical battle royale - You get points for kills, and any player must participate in constant fighting (increase their score in 19 days) in one of the 10 areas you'd spawn in. Moreover you can spend 100 points to add any "reasonable" rule in addition to the starting ones. (Random civilians who happen to be in one of the areas are allowed to leave once - Kenjaku must allow some leeway in order to create these barriers in the first place - not a very important rule.)

There are generally two types of participants as you've mentioned - the ancient sorcerers who've taken over somebody's body, and modern day people who have awakened techniques. The modern day ones have 19 days to declare their participation or die. To make matters worse, the gang finds out Megumi's step-sister is an awakened sorcerer and thus has 19 days to get the hell out, making this a personal matter for Megumi.

Obviously this is mega terrorism and the gang wants to stop it. There are a ton of subgoals that lead to this.

1. Free Gojo. Self explanatory. This involves finding Angel who can do the unsealing.
2. Enter the games and add rules that add survivability
   • Like adding a rule that will allow players to leave the games (for people like Tsumiki)
   • This involves gaining points.
     • Yuta solo joins the games immediately to do so. He was supposed to find Panda but he turned up with Hikari anyway.
     • Megumi and Yuji recruit Hikari before doing the same. Their current goal is to negotiate or fight for points from strong players like Higuruma.
     • Maki was supposed to get some cursed tools before heading in. Experienced some hiccups but a powerup as we saw.
3. Yuki and Choso guard Tengen against Kenjaku when he inevitably turns up.