It is not a Mars orbit. It's an orbit around the sun which reaches into the same orbital path Mars has. It will not interact with the planet in that way.

That's the plan, but this article is way too premature and the title is a little misleading. They want to put it into solar orbit at Mars' distance.

However, they are going to wait 6 hours to fire the second stage for a third burn which would actually put it in orbit. They want it to be exposed to radiation and test how well the booster holds up before the final burn.

No, it's a Martian transfer orbit, albeit without Mars at the other end.

Meaning it could have reached Mars, they just chose not to?

Meaning that they didn't launch at the right time to arrive at Mars, due to where Mars is in its orbit currently. It'll pass through the imaginary circle around the sun which is Mars' orbit, it's just that Mars will at a different part of the orbit at that time.

But actually, it seems they decided to just empty the tanks and get as much delta-v as possible, and it'll go all the way into the asteroid belt as a result.

Yes, depending on time of year. They could probably have aimed to hit Mars, but stopping in Mars orbit would (probably) require another burn on the Mars end.

Regardless, like other posts have said, they haven't actually left Earth orbit yet. There's one more burn in about 5 hours.

It would reach it if they lined up the dates, yeah. Landing something on mars just wasn't the goal here