Since Linux users make up 1% of the market share (I'm not sure the % for gamers, but could be lower), I'll doubt they'll lose sleep over it.
The question is, if they get really rock-solid drivers for Linux desktops, would the effort carry over towards entering the market for graphics chips in other things that run Linux like Android tablets and phones?
There is no market for graphics chips in those things, only SoCs which converge graphics with the CPU core. nVidia has an ARM SoC product like that, but AMD doesn't. AMD is sampling ARM server chips but has not even announced a mobile part. Meanwhile, nVidia is on what, their third or fourth Tegra? ATI actually used to make graphics chips for cellphones back when they did use separate GPUs; I used to find their cute little chips inside of Motorola phones, like V-series and RAZR. But now they don't, because they have nothing to offer.
I've been a proponent of AMD for many years, but what we're seeing now is the middle of the end. (The beginning was when they revealed their new architecture and it was... meh.)