In order to play games like the pros on your iPhone, you are going to need a decent, low latency controller. The Razer Kishi V2 is worth a look. It is an extendable game controller for iPhone that lets you play all kinds of AAA games. It comes with microswitch buttons, analog triggers, and programmable macros.
This controller has a Lightning connector and supports pass-through charging. Not sure which games are compatible with it? That’s what the Razer Nexus app is for. This gamepad is ready for PC and console game streaming.