Modern works like John Gardner's Grendel are difficult to categorize in terms of genre. Some works, like this are mixed and can be seen from different perspectives. In light of this, I would say that this work can be categorized as a fantasy novel or modern mythology. I would refrain from calling it an epic, like the medieval poem, because it is not in verse.
As for some of the characteristics, I would say there many interesting points. First, that it is from the perspective of Grendel is very insightful. The self-proclaimed monster is given a voice and at times he even elicits compassion. For instance, he is all alone. His mother is too old to be a companion.
Second, there are interesting literary techniques that are employed, like stream of consciousness. But what makes this most interesting is that it is Grendel's thoughts.
Third, the book is also very philosophical. From Gendel's point of view there is no meaning in life. In other words, there is a emphasis on nihilism.