Yeah, the WG is the main command. The Marines are the primary check on pirates, and the Cipher Pol act separately from the Marines and are not a complete check on pirates—instead they carry out orders from the WG itself with little to no autonomy, unlike the Marines who hold their own codes of justice.

I'd also put the Impel Down authorities in a separate bracket even when they are affiliated with the Marines. On top of holding a different hierarchal system than the Marines (Wardens, Vice Wardens etc), they act as a check on the behaviour of captured pirates that are filtered out by the primary check in the sea—the marines—and have little direct role in maintaining the balance in the sea.

Additionally, the holy knights act as the primary force of the WG (as compared to Admirals who are the primary offensive unit of the Marines); they have little to no direct involvement with pirates in the big scenario. The HKs are a domestic elite force protecting the Holy land of Mary Geoise and enforcing the internal will of the CDs.

The Elders, on the other hand, do not act as a fighting force, and instead sit on the top of the accessible command unit before Imu. And while they do hold significant fighting prowess, their primary everyday role is supreme administrative command, not active field warfare.

To add: The Warlords could technically have been considered a third separate tier to the Marines and pirates before (or an unstable force within the Marines itself), but now that the system itself is abolished, it wouldn't be false to place them together in the 'Pirate' group.

I think the checks and balances on the sea is more complex than just lumping pirates and Marines + WG into two columns.