These calculations are completely wrong. 7 Vrms into 1000 Ω is 7 * 7 / 1000 = 49 mW of power, not 7. Even taking into account the 10 Ω output impedance of the Essence One, a 300 Ω load allows for a maximum power of slightly more than 150 mW. With the HD650, that should be more than enough for anyone who does not want to go deaf.
You cannot simply calculate the actual power from the position of the volume control, there are variables that would need to be taken into account but you do not know, such as the taper function of the volume control and the gain of the amplifier. "50% volume" can really translate to anything.
It is a rather snobbish assumption that an Audio-Gd product is automatically better because the company is "specialized in headphone amps". There are many poorly designed and overpriced devices that are sold by small boutique audiophile companies. It may be better or worse than the Asus, this can only be found out by testing both.