What did you do? Install Docker & place the bios files and iso in the directories and run the game afterwards? ES has nothing to do with this since it just runs the PCSX2.start command and points to the game you want to run.
i have a fresh Installation now on my Homepc (I5 2500k, GTX 1080) Gamecube for example runing fine, PS2 iam in the same Situation i think.
I have Bios, and some Testroms in the right Directory. Docker is installed now. I start ES. Choose PS2, It goes short on the Kodi Screen Back, then it Start PCSX2 and give me the Warning GS Plugin Failed to open. I can press Ok and see then the Plugin Tab.
Under the Section "GS" i have the Plugin "GSdX (8.2.1 SSE4/AVX) 1.1.0 [libGSdx] and 3 other Options.
So i cant play PS2