Radon is easily mitigated. It is generated in the ground by radioactive decay, then diffuses through the ground driven by differences in air pressure. Radon is a heavy gas so once in a uniform pressure environment, it tends to fall -- that's why in a house it collects in the basement, where it is highest near the floor. It is pulled into the house by air pressure differences. Houses are generally warmer than the environment so, like a hot air balloon, they generally have lower pressure and suck in radon from the ground. Normally, an air conditioned house in the summer will have low radon, a heated house in the winter will have high radon.
Radon mitigation is basically putting a pipe between your basement and the outside air, so that pressure equalizes. If the house is low pressure compared to outside, the basement can suck in radon from an area of several acres. If the house is equal in air pressure to outside, it sucks in radon from a footprint equal to the footprint of the home. This will typically reduce radon levels by >90%.
A pipe and a drill to make the hole it fits through can be had for a few dollars at your local hardware store. The expensive "mitigation systems" are pipes that prevent bugs and rain water from coming in.
I guess the concern in your case is that if radon level is high in summer, it may be very high in winter; and the place has a mitigation system already which suggests the mitigation system isn't working.
It is odd that opening windows led to higher radon -- that suggests you had the counter well above the floor and the air circulation was pulling radon pooled near the floor up to the level of the counter. That's poor measurement practice, and the numbers they got may be unreliable.
But, I wouldn't be overly concerned about the home -- you can fix the radon problem easily. It's more a matter of who bears the cost of replacing or fixing a non-functioning mitigation system.
If it were me, I'd try to avoid inflicting hassle on the seller, and instead try to knock something off the price. If you can use this issue to reduce the price by $5k, you're way ahead because you can fix it yourself for $1k or less. I would get in the home cheaply, check the mitigation system for obvious clogs, then wait for winter and re-do the radon test correctly to see if the mitigation system is working. Then fix or replace it if needed.