Quoted from jalpert:
Not necessarily true that decent alignment at the top means it's lined up perfectly at the bottom.
This is definitely possible.
To get ink on the surface, you use a frame that has a special fabric stretched across it very tightly that has a specific thread count - the higher the count the more detail you get.
The image you're printing is burned into the fabric after it has been coated with a light-sensitive chemical that hardens with UV light. After using your film positive to burn the image in place, you wash out all the places that aren't hard. So, the ink you press on the screen goes through to the surface.
The reason you might get a misalignment at the top but not at the bottom has to do with screen stretch, as well as offset - if the screen is slightly higher off the surface of the playfield at the back than the front, it'll change slightly where the ink ends up. So even if registration is perfect, there might be misalignment with holes in the playfield.
You can see the exact press they use in this photo:
It's a manual one-arm press, with the screen (the aluminum frame under that cardboard) being attached to the hinge (where the hand knobs are) at the side of the playfield surface (towards the back of the table), so having variable offset on the other side is quite likely.
As you can see, it's a process that hasn't changed much in the last 70 years!