What is he referring to? (SPOILERS)

[Enkidoh]

Right, he was referring to the WoL being the 'Eikon Slayer' that eats Primals for breakfast (as far as the Garleans believe), and yes, that includes Bahamut. Information about the player's exploits were being constantly funnelled back to Garlemald through Zenos's forces in Ala Mhigo by Eorzean spies like Roalie, so he knows everything we've done, including our very lofty reputation.

[Moomba33]

I believe he was actually referring to Omega, who the Allegans used to subjugate Bahamut in the past.

He follows this statement by saying he will return to Ala Mhigo to see the "prize" for himself. You will see in the climax of Stormblood that the Garleans got a hold of

Shinryu. This seems to be the moment when he receives the report about the Garleans finding Shinryu and its state after its fight with Omega.

[Berteaux_Braumegain]

I believe he was actually referring to Omega, who the Allegans used to subjugate Bahamut in the past.

He follows this statement by saying he will return to Ala Mhigo to see the "prize" for himself. You will see in the climax of Stormblood that the Garleans got a hold of

Shinryu. This seems to be the moment when he receives the report about the Garleans finding Shinryu and its state after its fight with Omega.

This scene was left deliberately ambiguous in English. You're meant to assume what Enkidoh said so what Moomba said doesn't just come out of left field like a bizarre and foundationless plot twist. It has nothing to do with the Binding Coil. The biggest clue is that, even though canonically everything happens in the patch it was released in, there is no contingency line that prevents him from saying that if you haven't done the Coils.

Come back to this after you beat Stormblood's base story arc.

What you're seeing is Zenos receiving word that they've located Shinryu, who is still in Omega's bindings. This is why Zenos immediately rushes out of Doma and has Yotsuyu kidnap Krile so he can copy her Echo onto himself with Aulus's Garelans-magicks machine.

This is correct.