You Do Need power plug adapter while traveling from Mongolia to Liechtenstein.

Here is Why You Need An Adapter

The outlet and plug type used in Liechtenstein are C and J and in Mongolia are C and E. This is how they look like.

Mongolia

In Mongolia, outlets of type C and E are in use.

Type C

Type E

Liechtenstein

In Liechtenstein, outlets of type C and J are in use.

Type C

Type J