Does the word East have to have a period at the end when abbreviated?

yes just like you need to with south, S. ,north, N. and west, W.

Answer I work with wind directions all the time and they are simply abbreviated to E, W, N, NE, SW, ESE etc. Of course, it depends on context (my work involves meteorology so to context is obvious) but if you were writing prose you'd write the wind direction out in full anyway. The short answer is that the full stop is unnecessary, and arises from the US habit of applying them to all abbreviations (like Mr.) whether they actually need them or not.