Venus, which also lacks a meaningful magnetic field, and is 76 million miles closer to the sun and therefore has a much stronger solar wind, has a very dense, thick, soupy atmosphere.
How can dat be, eh?
That’s an interesting question. The constituents of their atmospheres are nearly identical too, so it is a good comparison.
In both cases, the lighter gasses like hydrogen are absent, but in Venus’ case, more of the heavier gasses remain. I think the key is that Venus is about 8 times heavier than Mars, so it would have 8 times the gravity, and thus retain more of those heavier gasses.