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.
[afaik] Unless the display driver or application being used applies a color profile or similar to compensate for the wider gamut, the color codes you use in your application will be sent to the display as-is. And in the display a specific color value (say E5) is no longer interpreted in the srgb scale but in the wider gamut scale.

So why does the display not interpret E5 in the srgb scale? This is because the values that the display adapter can send out are (typically) in the range 0-255 so in order for the wider gamut to be achievable the value 255 means maximum intensity in the wider gamut rather than the maximum intensity in the srgb gamut.

Should the display driver or application use a color profile, it can map the srgb values to the appropriate (smaller) wide gamut values and thus look "normal" on the display. Unless a wider scale is used than the typical 0-255 however then you will lose resolution in the process since a subset of the 0-255 scale will be used for srgb, for example 0-160.