It'ss easy to sound like a moron on twitter because all nuance must be edited out. The distilled soundbites are often more extreme than the original message, and often structured in such a way to make it difficult to argue with them. Leading with the idea that "millionaires didn't get all their money with credit cards" is an example of a common persuasive technique that's often used in advertising. You start off with something nobody can disagree with and then make a bad analogy with it to prove your point. Lots of us on here can see through this argument and might be pissed off by it a little, because it's blatantly manipulative and lazy.
He's given this statement many times over the years, not just on Twitter. It's a strawman he invented so he can beat the "credit cards are evil" drum. Literally nobody in the investment/personal finance world has made this claim.
How is this a strawman?
If you listen to his show, read his books, or otherwise have any idea what Dave Ramsey's target audience is you'll realize that a major portion of his audience has credit card debt/vehicle loans and otherwise are financially irresponsible.
For the vast majority of his audience credit cards have brought nothing but pain and harm.
It's also absolutely true that you don't become a millionaire by min/maxing credit card points. This isn't a strawman at all (I suppose technically back in the glory days of churning, you could have?).
No, not a straw man. I couldn't quite figure out which one it was. A red herring maybe?
It's a classic strawman.
Whether your statement is a strawman argument isn't about whether the statement you're making is true (it usually is, because...that's the whole point of a strawman) -- it's about whether the claim you're attacking is a claim that anyone is actually making. If you try to refute a claim, but you replace the claim the other person is actually making with a different claim that's easier to attack, that's a strawman argument.
Here, the claim Dave's purportedly refuting is that it's possible to
become rich via credit card points/miles. This is a strawman because no one is making this claim: rather, people simply claim that it's possible to
benefit from credit card points/miles. Dave rejects this claim because he thinks (or at least tells his audience) that no one, regardless of their financial situation, impulse control, spending, etc. should use credit cards. But instead of attacking the actual argument -- that people can benefit from using credit cards* -- he attacks the fake argument (the strawman) he set up -- that people can become rich from using credit cards. Like you already identified, it's lazy.
This isn't to say that the ideas underlying his tweet are entirely wrong; he's certainly right that plenty of people, and probably most of his audience, shouldn't use credit cards at all, and incorrectly believe that the benefits they're getting from points outweigh the costs they're incurring. But he's wrong in saying that nobody should use credit cards, and "rich people don't fall for stupid credit card tricks" is...very silly.
*He does attack this actual argument sometimes, but AFAIK his argument mainly boils down to "you're lying to yourself because eventually you're going to wind up carrying a balance." I can understand why he generalizes in this way -- it's probably true for much of his audience, and creating exceptions probably wouldn't help them -- but it's obviously not true for everyone, including lots of people around these parts.