The answer to your question is that "it depends." Please allow us to explain.
Idaho unemployment benefits are considered Idaho-source income, and thus are otherwise taxable by the state of Idaho, just like regular W-2 wages. So, for this purpose, it really doesn't matter if you are an Idaho resident, a Washington resident, a New York resident, etc. Idaho can and does legally tax your Idaho-source income, no matter you residency. The only difference would be the type of Idaho state tax return that you file: full-year resident, part-year resident, or nonresident.
That said, the crucial element in your case will be a determination of whether or not you need to file an Idaho state tax return at all. (If you do, then your Idaho-source unemployment benefits will be taxable by Idaho; if you don't, then you won't have to pay Idaho taxes on your unemployment benefits.)
For an answer to that, and to your original question as well, please refer to the following Idaho State Tax Commission webpage:
https://tax.idaho.gov/i-1039.cfm
Using the chart and the explanations found there, we can see that Idaho nonresidents need to file an Idaho state tax return if their gross income from Idaho sources totals more than $2,500 (in 2016). If you compare that $2,500 figure with the amount of your Idaho unemployment benefits -- along with any other Idaho-source income you may have had, such as W-2 wages from an Idaho job -- then you will have your definitive answer.
Thank you for asking this important question.
