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

Here is Why You Need An Adapter

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

Estonia

In Estonia, outlets of type C and F are in use.

Type C

Type F

Liechtenstein

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

Type C

Type J