The Boost license specifically states:
The copyright notices in the Software and this entire statement, including
the above license grant, this restriction and the following disclaimer,
must be included in all copies of the Software, in whole or in part, and
all derivative works of the Software, unless such copies or derivative
works are solely in the form of machine-executable object code generated by
a source language processor.
So no, you can't relicense code under the Boost license.
The project in question is rather confused about its license though; the top of the
README still says it's licensed using the Boost license, as does the
library's code itself. You could argue that the project as a whole uses the Zlib license, and includes Boost-licensed code, which is valid — but the code in question constitutes the entirety of the project...