I think an iPhone 6 is causing connection issues with other devices connected to my router (with Ethernet), how can I avoid it?
Troubleshooting is basically a process of elimination, but this one may be a little hard to do through the comments, so here we go.

TEST 1

Let's start by doing this test:


Switch Wi-Fi off in your iPhone settings (not just disconnect). 
Totally shut down the iPhone. 
Use your Wi-Fi as usual to play your real-time game for about a half hour and make a note of the results.
Switch the iPhone back on but do not switch Wi-Fi back on.
Use your Wi-Fi as usual to play your real-time game for about a half hour and make a note of the results.
Switch Wi-Fi back on in the iPhone and connect it to your Wi-Fi.
Use your Wi-Fi as usual to play your real-time game for about a half hour and make a note of the results.


After following the steps of test 1 you should have three sets of results to share back. This will greatly help you and the community to narrow down your problem, one way or other.

TEST 2

Okay, Power Line adapters are notoriously 'fussy' and it doesn't take much for something to interfere with the quality of their connection. Let's do this test:


Disconnect both ends of the Power Line connection, totally removing them from power etc.
Connect your MacBook Pro directly to the router via ethernet.
Ensure the iPhone is not connected to your Wi-Fi and play your real-time game for about a half hour and make a note of the results.
Now make sure the iPhone is connected to your Wi-Fi network and play your real-time game for about a half hour and make a note of the results.


Let us know the results.