This is no exception. In any situation where a molecule would be antiaromatic, it will "try" to avoid this. By adopting different bond angles or by bending out out of the plane, in other words by changing the geometry.
So, yes. The dioxine you show, with 2 double bonds and 2 lone pairs that could be part of the π-system, would be antiaromatic, *if the lone pairs would actually both be in the same plane as the lone pairs. But they don't have to; in fact, bending slightly out of plane would be beneficial even if antiaromaticity didn't play a role.
And as I mentioned, this is general. Any molecule that would be antiaromatic will distort to reduce/remove this. And every molecule with 4n π electrons in a ring will be able to do so. So it's a matter of searching for the possible way; a molecular model kit greatly helps here.