Laws vary from state of state. However, in Texas, the laws relating to DWI apply only to someone who is operating a motor vehicle in a public place. And, the punishments for DWI in Texas can be very severe. It is not clear that they work very well though.
Often, after some drunk runs over and kills someone on a bike, his record has been printed in the newspaper. Three or four prior DWI convictions. Been locked up for seven or eight of the past ten years. Gets out of prison, gets drunk, and kills someone.
When an officer in Texas arrests a drunk riding a bike, the charge is disorderly conduct, or public intoxication. Maybe two or three days in jail. So, a fella can get drunk and go to jail on Friday, and still make it to "Happy Hour" on Monday. A very light sentence compared to a motorist.
Thirty or forty people are killed riding bikes in Houston every year. About half those incidents happen after dark. And, it turns out that about half the cyclists killed riding their bike after dark were legally drunk. The motorist who killed the cyclist usually just drives away. But, when these motorists are caught, a significant percentage turn out to be drunk. So, a drunk motoriest killed a drunk on a bike. What are the odds?