The comparison does not necessitate the missiles being nuclear, if the missiles are otherwise capable of hitting essential Russian infrastructure in a short time. For example if they can shoot down Russian missiles, they in effect remove Russia's ability of deterrence; hypersonic missiles can hit key targets (buildings) within minutes.
NATO has placed troops close to the Russian border in military exercises, warships, and aircraft. They have armed and trained Ukrainian forces, aiding them in the attack on the Donbas-region. The defensive missile bases could from a Russian perspective be equipped with hypersonic or nuclear missiles, as the bases in Romania and Poland in particular are capable of firing such missiles, and as there apparently has not been proper mutual inspection of these sites, so as to reassure Russia. To my understanding such missiles have been placed throughout the last three decades in European countries.
What all of this appears like from a Russian perspective is that they are increasingly being surrounded by NATO weaponry and troops. It may be that I'm wrong and Russia wants to conduct imperialism, but I'm not going to be convinced by unfounded assertions of Putin's evil.
Now, the assertion that Russia is acting with Nazi-like ideology is frankly laughable, most of all because of the clear fact that central parts of the Ukrainian military and government are literally, self-acclaimed Nazis. Now, they hold small yet notable parts of the government, but it seems clear that they have the capability of intimidating and killing any opposition. They are in control.
The German Nazi' in WW2 were mainly defeated by Russians, and while the government in Russia is authoritarian, calling it Nazi-esque, while ignoring the clear Nazi faction of Ukrainian government and military is simply ridiculous.
My main sources are as follows:
https://thegrayzone.com/2022/03/18/pentagon-doug-macgregor-russia-ukraine-war/
https://www.newsweek.com/us-russia-nuclear-arms-race-over-and-russia-has-won-581704
https://www.energyintel.com/0000017f-307c-d3e7-a17f-f1fdfee40000
https://www.energyintel.com/0000017b-a7d6-de4c-a17b-e7d607180000