Why does this chart seem to show airports with magnetic variation up to 90 degrees?
How do you think "the figure seems to show an extreme variation of up to 90 degrees"?

I don't think you're understanding that diagram correctly.

There is nothing close to a variation of 90&deg; anywhere that is populated.

The angle of the curve has nothing to do with how strong the variation is.
All points on a single curve share the same variation.  If you find a 10&deg; variation on a curve, and trace that curve a thousand miles away, that point will also have a 10&deg; variation.

Look at about Washington DC, with -10&deg; variation.  Follow that curve all the way down to the middle of South America.  That point also has -10&deg; variation.

Look near Denver, CO, where it is +10&deg;.  Follow that curve out to near eastern Hawaii.  The curve there is almost due East-and-West, but that doesn't matter.  That area also has +10&deg; variation, because it is on the same curve.

The bold curves are at 10&deg;, 20&deg;, 30&deg; etc variation.
The red curves have a positive (east) variation.
The blue curves have a negative (west) variation.

All of this information is in the legend at the bottom of the map.