My Switch, which was pre-ordered from a big box store, came packaged differently: the Switch and controllers were both in those white foam slips. I appear to have been too lazy to throw them away -- they're still stuffed in the box, where I put them in my haste to get playing.
(I also remember peeling off a screen protector, though I was either un-lazy enough to throw that away, or I'm mis-remembering.)
Did you buy your Switch from a retailer, OP, or from someone on ebay? If the latter, I suspect that you got a second hand unit. Since people have reported seeing packaging like yours in unboxing videos, its possible that you have someone's review unit ...