The felt is attached to a rubber sheet. (You can't push as hard on an assembled ball as you can on the sheet material). And since you can't cut a sphere out a single sheet of material, there has to be a seam somewhere.
In the past, the sheet was cut into a "clover leaf" pattern that was then folded and assembled into a ball. Later, it was changed to the modern "half shell" pattern (which International Tennis Federation says was to increase the uniformity of the ball).
The rubber seam replaced stitches in the older balls and joins the pieces together.
I missed this part of the question:
the stitches definitely affect the movement of a baseball. Does the oval affect the movement of a tennis ball? Or would a tennis ball move the same way even if it was covered completely in felt?
A baseball is mostly smooth with a set of seams that can be oriented in a few different ways.
My suspicion is that the reverse on the tennis ball (a small smooth patch) has significantly less effect.
I found one paper on tennis ball aerodynamics. Tables 3 and 4 at the end compare lift and drag on a modeled sphere and a modeled sphere with a seam. The numbers are very similar and the effect of the seam is not called out in their conclusions.