Mixed Pairs Windshield Scraping. Judged on speed, completeness, style and degree of difficulty (using a herring instead of a credit card.)
I for one would enjoy watching ice basketball.
(Since Czarcasm already said this, team snowball fights would also have promise).
I think there’s a 50km cross-country skiing event, which is longer than a marathon.
(Which, yes, is a sliding event. I just think it’s interesting that the Summer Games marathon is not the longest Olympic distance race.)
One upside of the sliding and snow thing is the winter Olympics are much faster than the summer ones. Because sliding on ice can be lower friction than rolling on even a smooth hard surface. And crashing on snow can be a lot softer than crashing on dirt. Fast makes for exciting to watch.
But it is interesting that so much of the winter Olympics are played on a slope and substantially everything in the summer Olympics is played on a carefully leveled surface. There are exceptions in both games (e.g. ice hockey and whitewater kayaking), but the general rule stands.
Absent winter sports…
Anti-curling: sliding a chunk of ice across smooth concrete with strength and precision.
Ice swimming: just like regular swim events, but the water maintained at a near freezing temperature.
Ice climbing: using crampons, augers, picks, etc to surmount an icy incline in minimal time.
Igloo building: construct a shelter from snow and ice. Points for size of enclosed volume and maximum weight it can support.
Icicle fencing
Real Olympics are done naked.
Really brings doubles luge to a whole new level.
The 100-meter dash through the snow on a one-horse open sleigh.
I used to race XC skiing in high school. The best part of the ski meets was the massive inter-school snowball fights after the races. We used the buses as shields. And the bus drivers.
The new to Olympics Ski Mountaineering there is a section where they run up a hill, but it still involves significant sliding.
Brian
Doing donuts (or, depending on your local dialect, “doing Cheerios” or “whipping shitties” 
)
I think there’s a 50km ‘walk’ (the funny hip swinging one) in the Summer Olympics too.
Hopefully to the music of Kate Bush.
Perhaps some sort of gymnastics vaulting thing where the dismount ends up in a snowdrift and the score is based on the quality of the snow-angel that is imprinted.
Are you sure about soccer? I bet they would not call it that, sounds ridiculous. Ποδόσφαιρο does not sound like that at all.
Makes telling the teams apart quite a challenge.
Sliding is important, but the real points are scored breaking your neck, when the sliding stops.
I vaguely remember some comedy / spoof movie from the late 1970s (Network?) that included a scene of the World Sex championships. Or maybe it was the sex event at the Olympics.
But anyhow a couple was going at it and the announcers were using their golf whisperer voices to point out the moves to us home viewers and critique their performance. Scored on a 10 point scale just like gymnastics.
Of course the camera work was PG+ even if the topic was decidedly R. But it was a great concept for a skit and I thought at the time it was well-executed.
Possibly a skit in The Groove Tube (1974); as Wikipedia describes it:
I bet you nailed it in one. That’s certainly the right year +/-1.
YouTube has a bunch of clips from Groove Tube (that I didn’t watch), but they sadly seem to be lacking this one. Darn.
YouTube also had a reference to Kentucky Fried Movie. Which was contemporary and similar in concept but per wiki doesn’t have a scene much like I’m recalling.
Not any more, 2020 was the last time it was held. It was replaced with a mixed relay at marathon (42km) distance.
Of course! here’s a painting of Socrates playing for the gold medal against the Spartans:
I understand Leonidas was a very good midfielder too.