It isn't twill, poplin, herringbone or broadcloth. That pretty much sums up the typical types of shirting. So I would agree that it is probably pinpoint oxford.
Yes, it's a pinpoint Oxford. Judging from the label, it's perhaps 15 to 18 years old at least. It was made before Brooks Brothers shifted production of their pinpoints to Asia.
Brooks Brothers makes (and has long made) their must-iron, button-down pinpoint Oxford shirts in the following colors: white, light blue, ecru, light pink, blue stripe and red stripe. You have one of the older blue-stripe pinpoints.
So do I. With that kind of label.
Purchased around 2002-2003.
A must-iron, made-in-USA pinpoint from BB. Good-bye to those days. I remember when I'd take for granted the "Made in USA" label on shirts and trousers and stuff.
(I just reminded myself of a joke I read on a refrigerator magnet: "I'm old enough to remember when people would go an entire day without taking a photograph of something.")