No, an alcohol based DUI is not a "Drug" conviction. A Rx meds or illegal drug DUI conviction may be different in the employer's eyes. However, if WY is a at-will or right-to-work state, the employer may still fire your boyfriend is he/she so chooses. You may want to contact a labor law attorney to answer those questions.
Wyoming is an "at-will" employment state, but that could be modified somewhat by the existence of an employee handbook. It is a legally complicated analysis that also depends on the effectiveness of the employment disclaimers. Your boyfriend may also need to review the definition of "criminal drug statute" if he remains aggrieved.
I am licensed in Wyoming only. The legal analysis of any situation depends on a variety of factors which cannot be properly represented or accounted for on a web page. The information is intended as general information only, and is not intended to serve as legal advice or as a substitute for legal counsel. If you have a question about a specific factual situation, you should contact an attorney directly.