Why are laptops grounded to earth via 1E6 ohm resistance and desktops not?
The diagram below is based on the one you provided in your duplicate of this question. Not only are duplicates not alloeed they are a very bad idea as exactly what has happened here occurs - information is spread over two questions.

Your diagram was not of a power supply but of a line filter and it was left for right swapped.

I have rearranged it here and changed it to represent a power supply.
AC mains is connected at left.
DC low voltage is supplied at right.
The two series capacitors are the "Y" noise suppression capacitors required by most regulatory authorities.   

IF the green dotted ground connection is connected then the centre point of the two capacitors is at ground, as is intended by the designers.

IF the green dotted ground connection is NOT connected* then the centre point of the two capacitors is at mains/2 at an impedance set by the two capacitors.

If a 1 megohm resistor is connected as shown it provides an electrostatic "bleed" from the laptop low voltage ground to either mains gtround or mains/2. Either will discharge electrostatic charge. 

If the 1 megohm resistor is replaced by a hard link then if the green dotted earth connection is absent* then the laptop ground will be connected via the capacitors to Vmains/2. The impedance is low enough to cause very unpleasant but technically not life threatening shocks. It is also entirely adequate as a means of semi-random;ly destroying equipment connected to the laptop. 

*Mains ground may not be connected because a 2 wire power cord is used, or a 2 pin plug is used, or a 2 wire mains socket is used, or because Murphy wanted to have fun. Using the 1E6 resistor rather than a hard link tends to give the best of all worlds in most cases.