Learn Farsi: شنزار در شرق این نقشه است. - The sandy terrain is in the east of this map.

It combines شن (sand) with the suffix -زار, which denotes a place abundant in something. You will see this very common suffix in other terrain words like علفزار (grassland/meadow) and لاله‌زار (tulip field).

Why is there an Ezafe after شرق when the next word is the demonstrative این?

The Ezafe links شرق (east) to the entire phrase این نقشه (this map) to mean "the east of this map". Even though demonstratives like این do not normally take an Ezafe before the noun they modify, here the entire phrase این نقشه is acting as the possessor, so the Ezafe connects them: shargh-e in naghsheh.

Could I use خاور instead of شرق to say "east" here?

You could, but it would sound unusually poetic or formal. While خاور does mean "east" and is famous from terms like خاورمیانه (Middle East), شرق is the standard, everyday word used for compass directions and maps.

Doesn't نقشه also mean "plan" or "plot"?

Yes, نقشه is the standard word for both "map" and "plan" (as in a scheme or strategy). However, the surrounding context of geographic terms like شنزار (sandy terrain) and شرق (east) makes it immediately clear to a Farsi speaker that a physical map is being discussed.