Either vs. among
Solution 1:
You are right in saying that, strictly speaking, either is used for two options and for two options only. That's what the dictionary will tell you and that's what we're used for when using the word in various situations.
However, people use either for more than two options, just as you presented in the example from your local newscast. A sentence is not difficult/impossible to parse when either is followed by more than two options, so your audience won't have any problem understanding your words.
If you want to be strictly grammatical and completely proper, say:
1) either/between for two:
You can choose between skiing and snowboarding.
You can choose either skiing or snowboarding.
2) (nothing) for more than two:
You can choose skiing, snowboarding or swimming.