So, you may have better luck on /r/editors or /r/videoediting, but I'll take a stab at it anyway.

Actual oversaturation would mean you're compressing the color information at the top end. So, take this, and imagine everything getting squished toward the top. This will often also result in noticeable artifacting, as the differentiation between similar colors is lost.

What you're seeing from video from the 80's/90's is probably the result of a couple of things. 1) Style. Experimenting with vibrant colorscapes was kind of more of a thing, especially in the 80's. (See the Saved by the Bell open.)

2. Degradation. So... depending on what the original was shot on, how many formats it has gone through since then, and what you're watching it on, you're probably seeing a very different image than the original. An older example of this is very old music / voice recordings. You know how we think of them as being high pitched? That's only because they were recorded at a slightly different rate than they tended to be played back in later dubs.

Some of that is simplified, maybe overly so. And some of that is guessing based on some half-remembered film school classes. But it's in the ballpark.

It's actually two different subjects. Both of them basically are basically trends.

Deee Lite was born in the clubs of New York in the very late 80's - Early 90's. The club scene back then was full of bright colors, including neon. If you look at other club acts like Deee Lite, you'll see bright neon colors. Vanilla Ice, Black Box, C & C Music Factory, MC Hammer, all had bright or flashy colors.

Even the grunge trend still had bright colors to it. Nirvana, the Red Hot Chili Peppers, Pearl Jam, Temple of the Dog all had one or multiple members that wore bright colors, not necessarily neon, but still bright.

If you look at Heart Shaped Box by Nirvana you'll see both the bright colors and the saturation.

MTV was incredibly influential at the time, I think more back in the 1990's than it is now. The musicians and seeing videos influenced style, and that style changed depending on what your preference in music was.

The Game of Thrones video looks really similar to Xena Warrior Princess. It's actually the first thing I thought of when I watched it.

As far as the saturation trend of the last 20 or so years, this explains the editing process and why the saturation looks like it does.

Maybe try watching the same show on a period correct TV and see if it still looks over saturated.