From the airport, take the shuttle called "Rhône Express", it will bring you to Part-Dieu Train Station : there you can buy your ticket . Note that if you buy the tickets two months early, you have a better price : 20€ for round trip ticket.
Once at the station, buy a subway ticket (1.70€) and go to Charpennes.
Switch subway at Charpennes, to take the "Métro A" to Perrache. Step down at Cordeliers Station, you are one minute away from Gamespirit by walking. Note that Gamespirit is only 30 minutes away from Part-Dieu Train Station by feet.
Perrache Train Station
Take "Métro A" to Vaulx-en-Velin - La Soie, then step down at Cordelier Station, Gamespirit is one minute away by walking then.
From Perrache Train Station, Gamespirit is 30 minutes away by walking.