This is more a question for a programmer.
Is unit testing something that is done with games? If it is, is there normally something built in to the engine to facilitate it?

Programmers don't roam these forums as much as we the designers do... so I'll step in and ask what you mean by 'units'. AIs / characters / enemies?

Unit testing is automated testing of the code to make sure that it does what it should. It's basically code that checks the code is correct.

there are some tools to do this in videogames, it is usually done to do stress testing, for example leaving the game running all night playing against itself to check stability and memory management issues, it can also be done to test performance, like programming an AI to wander through the maps logging when the FPS goes under certain values... that kind of things
We have used this kind of code from time to time, when trying to find some specific, hard to find, bugs or memory issues, but some developers use it intensively to test their games
I hope this answered your question

Yes it did, thanks. So I guess most of testing is manual then?

Yes, for the kind of games that we made so far, manual testing has been the best option. (its always needed to find most of the bugs, since usually unit testing code will always do the same, over and over, we need to step out of the box to find most of the hard to find bugs)