How do I fight the CEO of Square Enix in 3C3C1D119440927?

In order to fight Yosuke Matsuda, you need to talk to a relatively inconspicuous Resistance member in the third arena (the one in the Flooded City). It's worth noting that, in order to find her, you will need to have completed through the rank S challenge at this colosseum (that is, you need to have beaten that challenge, not just unlocked it).

Inside the actual arena, to the left of the entrance and at the top of the stands, is the "Resistance Secretary."

Talking to her will prompt her to ask you if she can help with anything. You will need to select the "I want to fight you-know-who" option 3 separate times for her to decide to allow you to fight him.

After this, she will ask one last time, saying that the fight will break the immersion. If you choose "Immersion schmimmersion!" you'll fight Yosuke Matsuda.