You Do Need power plug adapter while traveling from Western Sahara to Saudi Arabia.

Here is Why You Need An Adapter

The outlet and plug type used in Saudi Arabia is G and in Western Sahara are C and E. This is how they look like.

Western Sahara

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

Type C

Type E

Saudi Arabia

In Saudi Arabia, outlets of type G are in use.

Type G