200dpi on a laptop screen would ideally need 1.6x scaling, not 2x. It could vary between 1.4x to 1.8x but definitely not 2x. Not sure what's wrong with that website.

At 13.5 inches, it would've been better to take a page from some Surface laptops and go for 3000x2000 or 3200x1800, depending on the preference for aspect ratio. At ~260 PPI, 2x scaling works fine.