Weird. Seems like a graphics card thing. Or a graphics driver thing.
You seem to be using a graphics driver from Microsoft. If you have a Radeon GPU, you should download the official drivers from AMD.
But if it's a 3400 series card, I suppose it would be a little quirky. Still, you could try updating: http://support.amd.com/en-us/download
Make sure you pick the right one in the dropdowns. It should be something like Mobility Radeon HD 3xxx series. Your GPU seems a little old. The very latest driver might not be the one you want. The site will let you know though.
I've seen Spine run just fine on several Windows 8 and 8.1 desktop setups.
I hope they can make sense of the log from the second computer and help you out.