The card has power limit below the FE edition. 650 will be perfectly fine given the assumption of a 65 W CPU and no 1-2 SSDs

I'm pretty sure the companies selling grafikkarte are putting bigger values than necessary because they must "ensure" the system is runnable with whatever you buy so that the customers can't complain (they can next say "but oh look I told you it need 750W"). If I were you, I would try first to run the system with what you have and see how it goes.
Moreover, you could look at https://pcpartpicker.com/ other people builds and you can know what works and what not.

The recommended 750 watts refer to a specific CPU configuration, which you can find on the Asus website. The more components (e.g. hard disks) you have and the more power these components need, the more power the power supply must have. I use a 700W power supply together with this graphics card and have no problems.