First of all, the Earth is tilted 23.5 degrees with respect to its orbital plane.
Second, the Earth's orbit is not a circle but an ellipse. Perihelion occurs January 2nd.
If you were observing the analemma from another planet, say Jupiter, its appearance would be different. Jupiter is tilted only 3 degrees from the perpendicular, but has a fairly elliptical orbit, so the solar analemma appears there to be a simple oval.
On the other hand, the analemma from a Uranus-based location is a very wide and even figure-eight. Uranus is tilted past "sideways" to an angle of 98 degrees. Its orbit is about as elliptical as Jupiter's and more elliptical than Earth's.
The makes a nice picture, the best ruin left at the site. It's not very big, and its use is not at all clear, probably they sold shish-ka-bobs. It looks like a late addition to the site, one of the artistic anomalies that is created when a society is in decadence. Delphi was a favorite picnic spot for wealthy Athenians--they had everything just like the state fair. Racetrack, concessions, fortune-tellers, you name it. The sky is very clear and it is far enough from Athens that city lights are not much of a problem. The Grotto no longer gives off fumes, and the show is over.