PCSX2 cannot boot directly from a physical DVD drive. It expects an ISO/IMG file. The "browser" screen you see is the PS2 BIOS because no valid disc image is mounted.
GameName.iso.System → Boot ISO (full) → select your ISO.Config → BIOS.System settings to skip BIOS animation.Config → Video (GS) → Plugin Settings.Once the ISO loads, you'll see the game's own menu—not the PS2 browser.