Ah, that completely changes the game. If you are stuck using a live video feed cable (like an A/V or proprietary multi-terminal cable pushing analog video) instead of a proper USB data link, the computer is only seeing the camera as an external video source, not a disk drive.
Because the camera itself is trapped in that "reinsert the memory stick" error loop, the video feed you are seeing is just the live feed of the camera complaining about the card. It won't let you pull the raw image files off it this way.
Since the card is a 2GB unit, it is a standard, older FAT-formatted Pro Duo stick (perfectly sized for vintage hardware, so file system incompatibility isn't the problem).
Because your current cable configuration is a dead-end for data transfer, here are your best moves:
1. The 15-Second Contact Polish
Since you can't bypass the camera right now, you need to convince the camera to read it. Grab a pencil eraser and vigorously clean the gold pins on the back of that 2GB card. Blow off the debris, snap it in and out of the camera slot 10-15 times to clear internal oxidation, and see if the "reinsert" error clears. If it does, you can at least view the photos on the camera screen.
2. The Right Tool: A Dedicated Card Reader
If the camera slot or the card's controller chip is acting up, the only way to save those photos is to remove the camera from the equation entirely.
You need a physical USB card reader that supports MS Pro Duo. Standard modern readers from high-street shops usually only have slots for standard SD and microSD, so you'll want a multi-slot reader (often sold as an "All-in-1" or "Multi-Card" reader) that explicitly states it has a slot for Memory Stick Pro Duo. They usually run less than 10 online and plug straight into a PC or Mac via standard USB, allowing you to bypass the camera's errors entirely.
3. The Cable Hunt
If you'd rather get a proper data link, the cable you actually need for data transfer depends on the camera model. Older Sony Cyber-shots usually used either a standard Mini-USB cable (the chunky, trapezoid shape popular before Micro-USB took over) or a wide, proprietary Sony Multi-Terminal USB cable (like the VMC-MD1). A proper data cable will let the camera talk to the computer as a storage drive instead of just a video loop.
If the photos on there are critical, the external multi-card reader is easily the most bulletproof option to rescue the files without fighting the camera's internal hardware glitches.