The provisional HDR support doesn't do 10-bit-per-channel, but rather supports half-float extended-sRGB. This is a color space which coincides with sRGB in the range of [0, 1], but is defined for r,g,b values outside of [0,1].
The general scheme is that one specifies that the WebGL backbuffer be half-float, and then any color values written (e.g, by a shader) outside of [0, 1] are then interpreted appropriately by the compositor. If your output display is WCG, then values outside of [0, 1] allow you to draw colors outside of the sRGB gamut. If your output display is HDR, then values outside of [0, 1] allow you to draw greater-than-SDR luminance colors
All platforms currently support WCG (although the final output buffer is 8 bit). Only Windows 10 currently supports HDR display and >8 bit depth output. What platform do you have in mind?