I thought I'd give it a whirl on the old ThinkPad T43 I'm using at the moment. I never really expect much from its tiny Mobility Radeon X300, but this was especially hilarious, and a most unexpected, refreshing change from the usual "oh, the disk LED is solid... again..." that I usually get. :P
FWIW, the http://aframe.io/ examples all work perfectly - I was actually slightly gobsmacked when I saw them, I can tell you with a fair amount of confidence that the simpler demos run on my system as fast as yours - so this GPU isn't a total lost cause with WebGL, and if it's moderately trivial to fix this, you'll net a small extra niche in your userbase (along with mobile users in 3rd-world countries using really entry-level smartphones and tablets).
If the fault lies with Phaser.io, and you feel like poking their ticket thingy, I'm fine with you passing the screenshots along. I'm also fine with testing potential fixes, if there's any room to explore there.
If your build environment can split out 32-bit Linux binaries without too much effort, I'd be happy to test that too.