Are you certain its the cores of CPU that matter here, if you have a lot of WebGL effects & particles, its going to be all on the GPU. The problem with older machines isn't that their hardware cannot handle it, it's simply because AMD & nVidia have stop supporting older gen of graphics cards so their newer drivers dont update for the older cards.
WebGL needs more recent drivers. It's different to something that uses DX9, since that's fine even on older hardware.
I have run quite complex games on my notebook, which only has a dual core, but it does have updated drivers for the integrated HD4000 GPU.
Something like a Pentium or Core 2 Quad from 5-7 years ago, is likely paired with a very ancient graphics card that just doesn't handle WebGL well, period.