I don't know of any specific devices available.
And in my opinion, taking a low-resolution interlaced source (S-Video) and displaying it on a non-TV monitor that isn't designed to accommodate this low-rez source will result in an overall worse picture. It would be an insult to your screen, and the picture won't be pleasing.
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Converting S-Video/Composite to DVI is an interlaced-to-progressive conversion, which is not a perfect process. If such a converter exists, you'll worsen the picture by either blurring the image, cutting the resolution in half, maybe cutting the framerate in half -- depending on the deinterlacing scheme chosen by the manufacturer.
If you can accept a mild picture clarity sacrifice, and you simply want to use your screen to play games because it's convenient (NOT because the screen is good -- it's only good for what it's meant for), then you should look into getting a TV capture device for your computer, rather than direct-to-DVI converter. They don't have any appreciable latency, and the output quality is more certain than a rare custom made DVI converter. The video from the TV capture device will display in a window in your OS, and you just expand the window to full-screen.