I am trying to install a floating shelf unit and the included wall anchors are these.
I've tried following the guide Here but it seems that mine have two tabs sticking out that stops them from folding "up" (towards the screw hole like in the video), however they do fold "down" (towards the vertex of the "V" shape) and was wondering if that was indeed the intended way instead, and would still work?
Throw them away. These are terrible anchors. There are better ones for every type of wall. I never use the hardware that comes with anything to attach to walls. Learn how the walls of your home are built and find great anchors and screws that you learn to use well and can rely on.
For drywall with wood studs (per your comment) and for light to medium loads without a lot of pullout (no TVs!) these IMO are the best. Easiest to use, most consistent, most versatile, least prone to failure. If you have a stud finder use it, otherwise drill a tiny pilot hole before using these plugs. If you hit a stud don't use the plug, just use a long wood screw by itself and ALSO not the one that came with your shelf ... buy good wood screws.
The ones you have do fold though they don't seem to want to. The center of the lower pieces are pushed upward while pushing the upper pieces down to form a slimmer post to insert in the gypsum board and the accompanying screw twists into the lower piece's hole tightly while moving the four pieces back to against the inside of the wall board.
But, I agree with jay613, in that the wall anchor he posted is better. It also is easier to remove and leaves a cleaner hole to repair when and if you do remove it. Don't over tighten it to the point of breaking the wall board or stripping the hole. A slight indentation in the wall board is what you should expect. I've used the metal and plastic (shown by jay613) for many years and some come in weight grades as to how much weight they should hold.