As for the mobile market, I haven't seen any recent figures so I won't comment about sales. I will say that from the benchmarks I've read the Tegra3 (2011) isn't as good as the RK3188 or the A31 (2012-2013). Mind you that Rockchip is running ARM's reference Mali so we might see a time in the next year or two that, like Intel's integrated graphics, Mali will simply be good enough for most consumers.
Seriously, I haven't seen the sales figures but considering AMD's poor presence in the Steam survey, I'd imagine consoles are probably their biggest cash cow right now.
They've been quite awesome that way and I've made the effort to recommend their hardware despite being forced to use nVidia's in some workstations.
All I can say is that they've owned an ARM license at least since 2011 and have been working on ARM servers for that long or at least a year. I've never heard they have any interests in Android but I suppose if their server chips proved surprisingly efficient and well preforming(which I doubt, no disrespect but it's still AMD we're talking about here), they might make an attempt on something portable.
As for SteamBox, that's linux so they have the drivers ready.