Yes, a systems engineer is a real engineer. It's an interdisciplinary field of engineering and engineering management that focuses on designing, integrating, and managing complex systems over their life cycles.
The role of a systems engineer, however, is not as firmly grounded in mathematics and science as in most engineering positions, such as electrical, mechanical, civil, or chemical engineering.
In particular, there are three major types of engineering - mechanical, electrical, and chemical. Many consider systems engineering to be a subset of mechatronics engineering, with mechatronics itself being a cross-section between mechanical and electrical engineering.