it is not the collar that puzzles me, but the buttons. Especially the ones that button all the way down.
I must admit that at first I didn't look at the pictures on the link, but just read the description. It says the shirts come button either halfway or full. The pictures show that the buttons are normal for a polo.
I wonder if they use a woven pique like in formal shirts, or a knit pique like in traditional polos.
I agree that if it has a full placket, it is no longer a polo but a knit dress shirt. I have several dress shirts and button-downs in both pique and jersey knit from Kamakura.
To me, polos are pullover shirts in a wool or cotton knit (jersey or pique) with buttons and a collar. Sleeve length, collar type and cuffs are variable, although if it has long sleeves it can be called a rugby. If it has a half placket it can also be called a popover.
Regardless of what we want to call them, I think these kinds of shirts are useful and definitely more stylish than just a standard polo shirt, and obviously better when it's a bit cooler outside. Brooks Brothers has one that is not unlike the one posted in the original photo.