It's not a moral argument. Skilled games don't typically fall under gambling laws.

That’s not true. Poker is only legal in a few states where gambling otherwise isn’t. (This was true still back when gambling was legal in far fewer states.)

A game that is both skill and gambling (of which there are many) still generally is regulated as gambling.

Poker is very much a game of chance. It falls in the (known) gray area of gambling laws since it has some skilled elements.

Much lower risk of people getting addicted to games of skill, and much less expensive for people who do get addicted?

It's the opposite on both counts. There is additional mechanism to get addicted - delusion of having an edge. If you're a bad addicted player you will also lose more (cause others have an edge over you bigger than casinos at their games).

Chess is the biggest game on Twitch, but getting addicted to it is pretty rare, and you certainly don't hear of people losing their house over their chess addiction.

Chess is a great game but it is rare to play for money because you have a very accurate rating system and no luck, so you know to a high degree of certainty who is going to win before the game starts unless the players are very close in rank. You can’t fool yourself easily.

With games of skill that also have a strong luck element (poker, fantasy sports, betting horses, etc.) you can fool yourself very easily into thinking the odds are in your favor when they are not. If you won you thought it was because you played better, if you lost you got unlucky, and if you don’t track it (even many professional players don’t) you may have a hard time even knowing after a long sample size where you stood.

Gambling relies on the ability of anyone to get lucky and win on any given day mechanisms rely on inconsistent rewards.

People don't play it for money. I mean specifically they don't bet on outcomes of their own games. This is what gambling is.

Chess wouldn't be as addictive anyway. You need a bit more luck ingrained in the game mechanics to trigger the addiction mechanisms. In games of skill like poker people get deluded all the time because they see lucky wins of their opponents and unlucky losses of their own. People are very bad at making judgements about probability so a lot of them get deluded into thinking "if only unlikely X didn't happen 3 times recently I would be ahead".

This happens in both poker and sports betting. In both games you can always pick some unlucky events (ball hit the post, referee gave an unjustified penalty, the only card falling on the river) and point to them to say "if only" while missing all the small lucky events on your side.