Actually, the LICENSE file is for their project (which amusingly, he seems to have gone from the original GPLv2 to MIT a year earlier: https://github.com/wordpress-mobile/WordPress-Editor-iOS/com...).

Even at that time, the source code included from the other project seems to have the embedded MIT license notice (e.g. https://github.com/wordpress-mobile/WordPress-Editor-iOS/blo...).

And in the README.md they have attribution, mentioning the licenses of the underlying dependencies.

tl;dr: The LICENSE file is for this project, not the underlying libraries they copy-pasted in (which other than say the png files, seem to have their MIT/BSD info in them).