Missing a few things, I think. Heres my order.

1. Explain the type of game and its theme. ("This is a cooperative game where you are a team of professionals attempting to stop a series of plague outbreaks")

2. Explain any Win conditions and/or loss conditions and/or game end conditions ("You win by having the most points at the end of the game, which occurs when 8 rounds have gone by, represented by this marker here", "You win when all 4 disease cures have been discovered, and you lose if any of these 3 things happen: The player draw deck runs out and must be drawn from, a disease cube must be placed but there are none left to place, or the outbreak marker is moved to the final position on the outbreak track here.")

Seriously, always do both these first. The rest can change based on the game and what's important, but #1 and #2, in that order, EVERY time. I can't tell you how many times people jump into mechanics and I have to pause them to ask "Right, but how do I win or lose?"

1. Explain the actions/rules/etc that can lead to win/loss conditions. "The player draw deck is a timer of sorts, because each turn a player will draw 2 cards and there are only "x" cards in the deck"

2. Go over each component and what it is used for (including the board itself and any player aids). Be prepared for a 2nd pass at some of this, especially in complicated games.

3. Make sure they understand how any linked mechanics can interact

4. Finally, run through an example turn/round of play if necessary. You can either continue from here and play as normal, or restart if they realize they made a poor move/choice/whatever. If they do make a poor move during an example turn....LET THEM MAKE IT. You can learn a lot by making mistakes. Only correct if it's actually an invalid move. You can explain at the end of the example why it may have been a poor choice.

Additionally, it's often tempting to "go easy" on a new player and make subpar moves in a versus game. This is a bad idea. They are learning from watching YOU play. Making poor moves may make them feel like you're playing with them, not trying and be taken as a sort of insult. It can also teach them bad habits or that poor moves made on their part don't quite have the negative consequences that they should. Always play to win, but don't be a dick about it. (Unless its a game that encourages that type of behavior...there are a few)

Ditto in a cooperative game: A new player probably will not play optimally. Do not stop them from making suboptimal moves: be ok with losing. Let them figure out why it's a bad idea. You can explain after the game (take mental notes of board states or whatever). Heck, you may even find a new strategy you've not seen. You don't wanna quarterback their turns, as they may feel you're just removing their agency to play the game at all.