open a konsole terminal and type xset -dpms and see if that works or not.
Wow - a word of wisdom from Texstar himself! I have to admit it, you were right on the money.
For the sake of betterment of the community, here's what this all means (based on my newly found knowledge mostly driven by
http://www.shallowsky.com/linux/x-screen-blanking.html). Apparently, some power settings and screensaver settings are driven by X, rather than any application (i.e. KDE) running on top of X. To find out what those settings are currently set for, all I did was run
xset -q and found that Display Power Management Signalin, better known as DPMS, was indeed enabled. Running the command
xset -dpms turns off DPMS. Running
xset +dpms turns it back on. And indeed, when I turn off DPMS on my system, then my screen no longer goes blank when I watch online content.
P.S. Interestingly enough, DPMS settings appear to be automatically re-enabled whenever power is applied/removed to the laptop.