In many situations, they just need a documentable/articulable (to a judge, later) reasonable belief that a crime was occurring in their presence, or in other situations that a specific crime had occurred and there was a reasonable belief that person had committed that crime.
Resisting arrest, and impeding official business of a police officer are usually arrest-able offenses almost anywhere.
Details vary by jurisdiction and crime, but ‘you need a warrant to arrest someone’ is an edge case, not the common case. In those cases, it’s also often an indictment or bench warrant.
If we normalize some dude in a mask and a baseball cap as someone that has the authority to arrest you and put you in an unmarked van, that represents a real and serious breakdown of trust and order in society.
ICE agents should wear a real uniform (ICE with their real name), have uncovered faces, and be required to show badge/authorization upon request -- otherwise members of society have to reason to trust them (or people who look like them).
"what they were doing" is attempting to illegally abduct someone. The comptroller's "impeding" was a demand to see the one thing that would make their request a legal arrest.
Instead, they arrested the comptroller without even a pretense of the law.