It sure does, you’re right. So does any “straight line” great circle too, so that isn’t super helpful. The equator has the same circle projection that 66° does.
Look at it from the side and it looks straight. If you’re sitting in the plane of 66°, the projection is straight.
I was trying to be supportive of @dbatten while explaining. It’s easy to get confused about what straight means on a sphere, since nothing is actually straight.
May apologies if I sounded knee-jerky. The intention was to show that a picture was a better answer to @dbatten's very legitimate comment.
The idea is to demonstrate that a "straight" line on a surface needs to be viewed along a normal to that surface at the point of the line you are concerned with, assuming the definition of "straight" is "don't have to turn when travelling along line on the surface". That makes great circles look straight, and non-great circles not.
On the contrary, latitude 66° on a globe looks to me like a fairly tight circle.
http://wordpress.mrreid.org/wp-content/uploads/2011/07/antar...