I would think most people are hurt from rollover and drunk mowing. Next being hit by a object coming from under the deck.
With all the safety switches on riding mowers I would not thing to many are getting cut by the blade.
I have seen guys mowing with a small child on the mower with them.
I have 100s of mowers and my step kids 10-12-15 and two grand kids 3-4 know not to ever touch a mower.
I am going to guess that 90% of injuries come from just being dumb
DUMB is the word here. Vast majority of "accidents" are simply operator error. Check out the Darwin Awards candidates for examples of dumb. Visited the consumer site mentioned and found the data was a 1987 report with the number of injuries listed as 18,000 not 80,000.
The number of unprotected operators would have been quite high in the 1980's. New, safer equipment is gradually added as older machines wear out and are scrapped. In the 80's I was still using 60's and 70's mowers without safety brakes or discharge shields because that is what I owned. It was in the 90's before I purchased a "modern" mower.
Other factors are the lawns that are being mowed. While living in a river town in Iowa, mowing my back yard involved tying a rope to the mower, starting the engine, allowing it to roll down the slope then pulling it up the slope and repeating the process until the grass was cut. Think there is an accident potential here? This was the normal procedure in some locations where the lawns are too steep to walk on much less push a mower. Ditch banks are all over the country. Current address had a deep ditch when we build our home 20 years ago. It required using a grass trimmer or risky push mowing. Installed corrugated culverts and leveled the entire front lawn to the street.