I hate to break this to you, but you almost always have to design the cabinet around the specific hardware you buy. There's not much standardization in the industry. You can't just swap out one brand draw slides or another ... and I'm guessing this brand (style) died a long time ago.

You're almost certainly going to have to mod the base cabinet to support modern draw slides.

But don't just buy something, and hope you can make it work. Look online for three or four options, and download the install instructions. See which style will be the easiest to use based on the cabinets that you have.