Actually you skipped a lot of details there.
When you click on a mouse button, micro switch under the button registers this. (as electric signal) which is then passed to the processor in the mice. (yes, they have one too) which then sends it to computer through cable or bluetooth or whatever. (depends on the type of mice)
If it's usb (most common at this day) then USB controller gets the click event from mouse and forwards it to the OS (we can assume windows)
Edit: Mouse actually records it as separate events like button down, button released and OS decides what it does with them.
Computer then sees that mouseclick happened, checks the coordinates where the mouse was at and acts accordingly. (coordinates of the cursor are NOT stored on the mouse)
since most still have it as default, needing double click to open it, you only selected the icon by single click.
thus you would need to do two clicks in certain time (set in mouse settings) to count as double click which equals "run"
Since target of chrome's shortcut (if we assume 32 bit version) is "C:\Program Files (x86)\Google\Chrome\Application\chrome.exe" it does just that, runs said exe.
Said exe contains a lot of coding, which I wont go into