The schematic is only partial but it looks to me like they are using the mains "neutral" as "system ground". To add to the confusion it looks like they are using the "earth ground" symbol to represent system ground.
The microcontroller only cares about voltages between it's pins. As long as the voltage between the pins is acceptable the microcontroller will be fine. The fact that in some cases the whole circuit will be moving up and down at 50Hz relative to ground doesn't bother it**
In designing an electronic system with logic controlling mains there are essentially two options. One option is to refer the electronics to the mains supply (either live or neutral) and put safety isolation between the logic and the user. The other option is to have the logic either floating or reffered to mains earth and put safety isolation between the logic and the mains.
In large volume the former approach is often more economical as it avoids the need for a bunch of isolation components. Yes it means your buttons and displays need to have safety isolation but that can often be done at very little cost through careful design of the front panel.
* As you point out in your comments on Olin's answer the "Neutral" connection on the machine may end up connected to either Live or Neutral as some countries use unpolarised plugs.
** If the frequencies were much higher then moving up and down relative to earth ground could be an issue as stray capacitance is everywhere.