Not sure I agree with the basic premise of this article.
your game will run much slower and behave far more erratically.
[citation needed] - what do you mean by "erratically"? Isn't the issue you followed up with purely to do with Tiled Background?
Power-of-two images are pretty much a necessity for tiled backgrounds, because that's the only way you can get perfect seam-free display, and it's faster too. Outside of Tiled Background, the only issue with using a non-power-of-two texture is it uses slightly more VRAM (ie. rounds up to a power of two size as you say). For sprites and other objects, Construct never stretches the textures, just places transparent gutters around the edges, so there's no difference in visual quality whatsoever, the performance will probably be identical if the same number of pixels are drawn, and there should be nothing "erratic" about it. The conclusion should be "be aware you might be using more VRAM for non-power-of-two textures - and remember Tiled Background is a special case", but your conclusion of "always use power of two textures" is over the top. Also, I think GPUs from the past five years or so can all safely handle 1024x1024 textures, since 512x512 is still pretty limiting. Remember Construct often creates window-sized textures for effects and such, so even for a 640x480 game, a window sized texture is rounded up to 1024x1024.
Edit: don't mean to totally trash your article though it's a fairly important engine point that's worth knowing.