7 USC § 1a(37) defines an "organized exchange" as

> [A] trading facility that— (A) permits trading— (i) by or on behalf of a person that is not an eligible contract participant; or (ii) by persons other than on a principal-to-principal basis; or (B) has adopted (directly or through another nongovernmental entity) rules that— (i) govern the conduct of participants, other than rules that govern the submission of orders or execution of transactions on the trading facility; and (ii) include disciplinary sanctions other than the exclusion of participants from trading.

And 7 USC § 1a(51)(A) defines a "trading facility" as

> [A] person or group of persons that constitutes, maintains, or provides a physical or electronic facility or system in which multiple participants have the ability to execute or trade agreements, contracts, or transactions— (i) by accepting bids or offers made by other participants that are open to multiple participants in the facility or system; or (ii) through the interaction of multiple bids or multiple offers within a system with a pre-determined non-discretionary automated trade matching and execution algorithm.

(7 USC § 1a(51)(B) then follows with some exceptions to that definition.)

In short—an "organized exchange" is defined as a type of "trading facility". To count as a trading facility", whether of the "organized exchange" type or not, you must either accept bids or offers from other participants yourself or else deterministically match and execute those bids and offers.