It's a fake BIOS/DOS bootscreen to parody the startup of the original DOS demo (the c64 version of the demo does something similar).

It says DOS3.3 as a joke, because Apple DOS3.3 was a real, long-running operating system for the Apple II that predates MSDOS.

The actual demo runs no operating system at all, it's a custom bootsector designed by qkumba that can load arbitrary tracks off of a raw Disk][ floppy and is much faster than DOS3.3 or ProDOS and also requires very little memory overhead.

Thanks. I remember AppleDOS 3.3, and I remember it had no concept of directories (you had to use ProDOS for that, which didn't use the cd command anyway).

But as far as I know Apple DOS does not have directories (PRODos has), and neither have the cd command.

Ah, I misunderstood what you were asking. You mean the interface right at the start of the video, right? I don't know what that is, I assume some sort of custom firmware and/or hardware?