Yeah....if you look at that video you can see that he has LOTS more pixels in the image.
The image he is working on is 3840x5760px so his marquee area actually contains many, many, more pixels than your example.
If you download the Project Files for that tutorial and open up the image in PS, do the same marquee as the tutorial and zoom in so that you can see the pixels you'll find the exact same 'squared' boundary as in your example..
Remember, PS is a PIXEL based image editor......the PIXEL is THE most important thing in the image.....and everything that PS does relies on them.
One other thing to note is that things like the marquee boundary, (Marching Ants), and guide lines, your brush shape cursor etc etc are all Non-Scaling. That means that no matter how far you zoom into an image those things will not change their size...OK, the brush will but the line thickness of the cursor will remain constant.
These Non-Scaling elements are draw according to your SCREEN resolution and NOT part of the Image....so a 'guide line' is drawn using a single line of [ LCD monitor ] pixels and NOT a single line of IMAGE pixels.
Likewise all vector shapes are drawn using the screen pixels and are converted to image pixels when rasterised.
All the marquee tools also use the screen pixels until you finish the creation....this is why when you use the Polygon Lasso tool it draws nice straight diagonal lines....because its using the screen pixels, but when you close the shape the line jumps to being 'squared'.....because now its using the image pixels.
Get it? LOL.
Its not that easy to get your head around granted, but thats the basic jist of it anyways....just in case you wanted to know.
Regards.
MrTom.