Question: A wide gamut screen displays more than the sRGB color space.  

So why, with softwares that do not deal with ICC profiles, with a given color that has it's own place / value in the global color space, is rendered differently on a wide gamut screen than on a standard screen. 

I mean, the color that corresponds for example to the #E58C4E color, is at the same place on a reduced color space, or an extended color space. So a monitor that can display a large color space should be able to display correctly a color that is in a color space that is inside it, whatever the way it is adressed to it.

Answer: 
Actually, `#E58C4E`, if you mean the web color, is [defined to be in sRGB](http://www.w3.org/TR/css3-color/#svg-color). However, if you didn't mean that particular convention but rather "red:229, green:140, blue:78", it's a different matter, because the extremes (the "primaries") of each channel are different in different color spaces, so those numbers actually *do* represent something different in each space. (Arguably, that's what a color space *is*.)

The monitor has its own primaries (the native color space of the monitor), and a color managed system translates between a known profile for a given image and the native output. If the color space of the original isn't known, there's no way to guess at the proper translation.

So, another way of asking the question might be: why aren't colors from un-color-managed-applications just *assumed* to be sRGB and translated on the fly? From the monitor's point of view, that's easy: it has no idea about which pixel came from which application, so it wouldn't know what to translate and what to leave alone. The graphics driver level has the same basic problem. Going from the other side, un-aware applications can't do it, because they're unaware. So, that leaves the operating system's display manager to do it, and that's hard. 

So here we are.
**There is no global color space.** A color as you specify is just a triplet of Red, Green and Blue. Each component has a value between 0 and 255 (0 and FF in hex) which indicates how much power to give each LED for a given pixel (or phosphor in the days of CRTs).

**The scale is relative to your monitor and its current settings.** This is why monitors need to be calibrated. On a wide-gamut monitor the values are just spread along a wider color-space.

If you expected the color to display to be transformed into the display's color-space then you need to have at least a monitor profile for your monitor and tag your images with an ICC profile so that the operating system knows how to do the transformation. This of course will result in banding artifacts since precision is lost.