I really dont think this is legal without at least an AOW tax stamp.
It doesnt matter that it isnt vertical, its a forwards mounted grip. The rare integral grips that were built into the machine pistol versions of berettas 1911s and others are illegal when put on a normal pistol, and most of those fold out to be angled well forwards, definitely not vertical. They are legal on the original guns because the stamp for it being a machine gun nullifies the need for aow or sbr paperwork.
There also arent any vertical lines in the sig factory forward mounted grip shown in the graphic on the top right of his page, and I dont think anyone would argue that is legal to mount on a pistol.
Do it if you want. Don't bitch when the ATF kicks down your doors and takes you to jail. They are less than perfect, but you're inviting their presence if you do this, especially if you post about it on the internet.
They wont send you a friendly note telling you you're wrong, they'll just send you to prison.