There is nothing technically preventing the use of globals, it's more a matter of taste and choice of language.
The author of the tutorial is speaking from the point of view of using SDL from the c++ language. In C++ there is a strong emphasis on object-oriented code structure, including encapsulation and abstraction (i.e. hiding the details of an implementation behind a class structure).
The author goes into more details regarding global objects and classes in tutorial 7, which might be useful to get a better understanding of their design process.