Usually, in Linux desktops, the icon won't be taken from the exe file itself since there is no "standard" way to do it.
To associate an icon with an application you have to either create (and install) a .desktop file or use some other mechanism like, for example, doing Alt+Enter in the file manager to show the exec file properties and changing the icon there.
Note also that in both cases (and most others I know of) the icon has to be a separate file and in a recognizable image format (png, svg, ppm, pnm, etc.)