This screen protector is designed to be an anti-shatter protective tool because unlike the older Switch modes that use a plastic display, the OLED Switch actually uses a glass display so the screen protector helps prevent the glass from shattering into shards should it ever get broken when you drop it or from other accidents.
The good news is that this saves users from having to make an additional purchase for a new screen protector, but for those who want their own screen protector for whatever reasons, you’ll have to install it on top of the existing screen protector.
The company has confirmed to The Verge that installing your own screen protector won’t be a problem. The anti-shattering film will not interfere with the screen protector so you should be able to install an extra one without running into issues. In fact, Nintendo actually sells their own first-party screen protectors for the OLED Switch if you’re interested, although it is priced at $20 which is kind of pricey compared to third-party alternatives.