It's not a "sound card" per se... it does analog-to-digital conversion (which is essentially all an internal sound capture card or external
audio interface box does anyway). Having a "built-in sound card" doesn't make it a recording device. It's an audio input box, and the ASIO driver is what makes it possible for recording software on his computer to see the audio stream that comes out of the GS-10's USB port. The GS-10 doesn't write any of that audio information to disk. The software on his computer does.
Regardless, the GS-10 is a digital device, so whether it's good quality or not, his guitar signal is going through those A/D convertors just to get processed by the unit. If you feel the GS-10's conversion isn't as good as you'd get on a high-end card (which it probably isn't), then forcing the signal through a second conversion back to analog so you can re-digitize it with a better quality device makes no sense... you're not really going to preserve any signal quality. All you're going to do is compound the weakness of the GS-10's conversion. A digital signal chain is only as good as its weakest link.
The question is, will the difference between the GS-10's convertors or a high-end audio card's make an appreciable difference in the final recording? I would suggest that without a pro studio rig outfitted with all the best gear possible, the difference will be negligible. I'd go for the convenience and affordability of having an all-in-one device and record the digital signal from the GS-10.