I just saw the product link you posted, I have the Bluetooth model with the retro receiver.

SFC30 https://www.amazon.com/dp/B00Y0LUQFE/ref=cm_sw_r_cp_apa_YvqFAbVVYPHTN

Retro Receiver https://www.amazon.com/dp/B076B995TL/ref=cm_sw_r_cp_apa_axqFAbD0MBFJC

Of note I got the SFC30 for easier use for my kids (push the Green button) but again the parts are swappable with official controllers if you want to keep the purple scheme, or just buy the Bluetooth SN30.

I have one of these 8bitdo SFC30 controllers and I absolutely love it. I've used it so much over the last year and a half that I'm very likely going to buy one of their NES30 Pro controllers. I think the NES30 Pro is better suited for PSP emulation and for use with a lot of indie games I have on steam (e.g. Rogue Legacy, Binding of Isaac, Risk of Rain).