... it is thoroughly commented (in fact, one of the most commented codes I have ever seen). And 156 lines only.
After a study of a good 8051 textbook (or even better the tutorial - located on the left bar <--- ) you should be able to understand most of it. Just go step by step on the code, with a pencil in your hand, writing down on a piece of paper, which registers/memory positions changed and how.

You can use a simulator, it is more comfortable, but not necessarily more illustrative - sometimes too complex; and usually to learn how to manage with is much of boring and one might give up prematurely.

Jan Waclawek