As far as I can tell, it was punished severely, but not quite that severely.
I found Nevada's 1971 controlled substances statute, AB 107. "Marihuana" appears in Schedule I, the list of drugs which are most tightly restricted (Section 31, subsection 4(j)).
Section 65 makes it a crime to possess such substances. Under subsection 1, a first offense was punishable by 1 to 6 years in prison, a second offense by 1-10 years, a third or subsequent offense by 1-20 years. There were also fines of up to about $2000-$5000. There was an exception in subsection 3 for marihuana possession of less than one ounce: a first offense could alternatively be punished by up to one year in county jail, probably at the discretion of the prosecutor or judge. Second offenses were treated as a first offense under subsection 1, and so on.
Selling and distributing drugs including marihuana was punished more severely. Under Section 62, the punishment was 1 to 20 years in prison for a first offense, and for a second offense, life in prison without possibility of parole. If the drug was distributed to a person under age 21, a first offense was punishable by life in prison, but with possibility of parole after 7 years. There was no exception for small quantities of marihuana.
I didn't find a reference to the specific 25 year term you mention. It's possible that it comes from some version of the law as it existed before or after the 1971 statute; I didn't check. Also, marijuana was (and still is) also illegal under federal law; I didn't check what punishment federal law would have prescribed at the time. It's unlikely that the City of Las Vegas would have had separate laws; this sort of thing would normally be done at the state level.
As far as I know, this is in keeping with other state drug laws of the time, and given the prevailing politics, I'm not surprised by the law. Drug use was treated very differently under the law than the other "vices" you mention. It'd be outside the scope of this site to discuss the possible factors behind this, but you could perhaps take it to Politics.SE or History.SE.
Nevada eventually legalized recreational marijuana for adults in 2017, according to https://norml.org/laws/nevada-penalties-2/. It was not the first state to do so; Washington State had taken a similar step in 2012.