My assertion is that reducing government to "people-with-guns" is not useful, because there are non-force means of state coercion.

You say that without the ability to project force, then a response from someone being denied services is force, and when that happens, the government responds with force.

So be it. Yes, that's almost completely true. At some point, every single action can be trumped by someone with bigger guns, and everything recast into a force viewpoint.

There's a few which cannot and were not trumped by guns. Under the old laws, someone had to plead innocent or guilty before being tried, and lands could not be confiscated without trial. Giles Corey famously resisted the torture of being pressed to death, calling out "more weight!" instead of pleading innocent or guilt. As there was no trial, his lands were not forfeit to the government. Having the biggest guns didn't work there.

As a more hypothetical example, it's hard for you alone to force a doctor to do a quadruple bypass on you, because at some point you will be unconscious, and the doctor can simply stop working. You might try various dead man options, but the odds of success for you are very small. Nor can you and a thousand others, by threat of force, get people to build you a spacecraft to travel to the Moon and back - there are too many points of failure where a single person, through deliberate negligence, can stop that from happening.

In any case, a government does not need to claim a monopoly on violence, nor does civilization need that as a prerequisite. I pointed to the Viking sagas as a case in point. Look specifically at Grettir's Saga. It's acceptable to kill someone, so long as you are willing to pay the weregild. That's part of medieval Scandinavian law, which is not based on a central authority.

In this saga, the people involved could not settle on the payment themselves, so they consulted the lawman. (The lawman was the sole government office of the medieval Iceland.) Thorkel Moon decided on how the weregild was to be paid from the lands. In addition, the killing started because of a disagreement in who gained from a beached whale. The lawman decided "henceforth be it made law, that each man have the drifts before his own lands." Based on the previous paragraphs of the saga, which describe the violence between the different parties, I easily draw the conclusion that people decided it was better to follow that edict than to undergo the deadly fighting every time this might happen in the future.

Clearly civilization can exist and has existed where the government does not claim a monopoly on violence.

Even in US law, the government has explicitly stated that certain types of violence by non-state actors are explicitly allowed, and the government will not interfere. For example, parents are allowed to beat their children, to some extent, even when a government actor cannot do so.

Yes, you can recast this as the government allowing some sort of devolved violence, but as it's indistinguishable from saying that the government has a non-monopoly on violence, and there's clear examples where government didn't have a monopoly on violence, I conclude that your view is too reductionist to be useful.

"Laws either are backed by violence if you persist in violating them, or are ultimately irrelevant"

shrug Everything is ultimately irrelevant. The US will crumble and/or be replaced someday. All acts of violence any of us do will eventually be meaningless in the face of entropy.

In the shorter term, consider the US Pledge of Allegiance, probably the most recited socialist-derived words in the US. US law - the Flag Code - describes the pledge. The Supreme Court in West Virginia State Board of Education v. Barnette said that the government could not force child to state the pledge, as it was a violation of the First Amendment. Further court decisions said that a child could not be punished for not standing up for the pledge, and that recitation must be voluntary.

Thus we have a law which has no "guns" behind it. When teachers have tried to punish students for not saying the pledge, the government courts have reprimanded and fined the schools.

And yet that law has a coercive ability even though there is no state force. It's backed by social ostracism, yes, but that's certainly not part of "the government's monopoly on violence."