At first glance, it appears that the only styles missing are the styles that rely on a zoom level. When exported in MBtiles, your "map" is seen in a map context where you have zoom levels, and as such, your styles are rightfully applied. However, when exporting a static map, by default there is no zoom level applied during rendering.
I've snooped a bit and found this issue on TileMill repository, which would correspond to your problem: https://github.com/mapbox/tilemill/issues/1819
Unfortunately, the fix (under the form of a
static_zoom parameter in the command-line) doesn't seem to be in the last "official" release available of TileMill, but if you install it from the source on GitHub, it should be OK; something along the lines of
./index.js export help should tell you about this
Of course, another solution would be to comment out the conditions the zoom, to always apply the styles you want, and export afterwards.