Here is some evidence of what can occur when Mylar pop bumper protectors without stickum is used:
After some cleaning:
I know nothing about the history of this Gottlieb Snow Derby so I can't tell you if these pop bumper protectors are original or add-ons.
Dirt and grit CAN collect under the protector, causing wear, possibly even increasing the speed of the wear. Without the adhesive, these protectors tend to lift over time and no longer lie flat on the playfield - not an aesthetically pleasing sight.
Given a choice between non-adhesive or adhesive, I would choose the adhesive pop bumper protectors. Removing the pop bumpers and thoroughly cleaning and waxing the area under and around the pop bumpers is a must before putting on the adhesive Mylar pop bumper protectors.
There is another option that you might want to consider. It involves using the non-adhesive protectors and some rubber cement. It is experimental, so consider that carefully before you choose this option. If it doesn't work out for you, it should be fully reversible: