WebGL renders using the GPU, which means graphics rendering happens equally as fast as a native app. The difference is the CPU.
2D game performance is much more CPU-bound than 3D games. Basically, those performance tests measure how quickly the CPU can issue a draw call to the GPU, which has a lot to do with how fast the javascript engine is as well. The test machine in the blog post you linked to is very powerful: it's a custom-build quad-core Core i5 3.3 GHz, with an AMD Radeon HD 6570 graphics card. Laptops tend to have weaker hardware to save on battery, space and cost, even if the marketing makes it look as powerful as a desktop, so don't expect them to be like desktop performance. Finally, make sure your laptop is plugged in and not in power saving mode or it will be slower!
Also, bear in mind even 5400 is an excellent result. How many games ever have more than 5400 sprites on-screen at once? I'd even guess none at all, and your computer can still get 30 FPS even in that case. Even your worst result, 570 - how many games have over 500 sprites on-screen at once? Probably a minority. So your results are still pretty good! You're just not reaching the same standard as my extremely expensive, high-power development machine :)