Engines are significantly higher level than what we call frameworks in web dev, with a lot of stuff built-in and coding being a minor requirement. Traditionally they were even genre-specific: fighting game in case of Mugen, shooter in case of Quake and Source, etc. Also, in the case of Mugen, they are mostly data-centric rather than code-centric like a web framework.

Another interesting distinction is that engines can often written in one language but offer extensibility in another, like being written in C++ and having programmers write Lua or C#. Notable exceptions exist, however. In frameworks that's quite rare I guess.