The MIT license doesn't require source code to be published. It only requires that the license notice is kept intact. MIT-licensed binaries without source code are rare – no source kinda defeats the purpose of open source – but it's also not the first time I've heard about this construction.
Even for licenses like the GPL that do require source code, it's useful to look at who is subject to this requirement: only recipients of the license and creators of derivative works, not the licensor who created the original software. Thus, even a GPL-licensed binary without normal source code could legally exist in rare cases.
While you do not have a right to receive the source code for the MIT-licensed binaries, you can still ask. Often, such weird licensing constructions are created by people who are new to the open source community, often also new to how version control works. Therefore: don't demand source code, but kindly ask whether they would be willing to publish it. If GitHub issues are deactivated, you can often extract an email from the Git commit history.