I was wondering, what are the requirements that make contemporary authors / pieces of work contemporary?
There are no official requirements for contemporaneity.
There are two definitions for 'contemporary,' according to Merriam-Webster's. The first is, as follows: "happening, existing, living, or coming into being during the same period of time." The other delineates things that are "marked by characteristics of the present period." In regard to literature, the latter definition is most helpful.
When we talk about contemporary literature, we are talking about those works and authors who discuss how we live now. One of the reasons why the works of Jonathan Franzen are so popular, for example, is because he writes about how people's lives are contextualized by contemporary events, such as the Iraq War or environmental destruction.
Contemporary works are different from works that we define as "timeless," that is, those pieces that are relevant in any social context, or at any time. The works of Shakespeare most obviously fall into this category. Because his plays deal with very broad themes, such as abuse of power, tragic romances, and existential angst, he remains relevant. An author whom we read now might not be relevant one hundred years from now. To be "contemporary" means to be relevant in the moment.