some older intel graphics chips have abysmal linux support.
i did some quick searches, not sure if intel mobile gm965 is one of those.

anyhow, is it older?
if so, i think it basically comes down to what veerain said:

Someone else in another forum on here, don't remember which, was mentioning that media players won't play video correctly using hardware acceleration on a GM965, so maybe it's just a matter of poor hardware support.

Thank you; I did that also. And yes, this is quite an old chip but Intel/Linux seem to be supporting it still.

This does seem likely to be the case as Xubuntu does not exhibit the same behaviour on this laptop, so the problem does not seem to be in the kernel. Interestingly, Tumbleweed (installed on the laptop hard drive) does not crash under the same conditions, so that points to the problem possibly being in the KDE 4 libraries. I would just use Tumbleweed but it's a long way away from being ready for everyday use. For me, anyway.

But the big mystery here, is: why the flipping flip does opensuse 13.2/KDE run just fine on this laptop hardware when installed on an external hard drive?

It could well be poor hardware support, possibly in the KDE 4 libraries. But it's puzzling that opensuse 13.2 does not crash when installed on the external hard drive.