In steam's .desktop file there's a line 'PrefersNonDefaultGPU=true'. This
causes steam to render itself only on the non-default gpu, which will always be
the one not currently in use. Looking at the issues concerning this on the
steam github repository, this line was intended to make systems always use a
discrete gpu if available. However if you're currently already using video out
from your discrete gpu, this will make it render only on the igpu (not desired
behavior). Removing this line from the .desktop will make steam render on
whichever gpu is currently in use, with games still defaulting to the dedicated
gpu if available (desired behavior).

I would've submitted a fix for this myself but I'm not sure where to do so.