Can You Play NBA 2K13 on Xbox One?

No. NBA 2K13 is not backward compatible on Xbox One.

2K Sports did not submit the title for the Xbox One backward compatibility program. The series' BC support begins with NBA 2K16 (via NBA 2K16 being BC) and includes newer entries. NBA 2K13 remains playable only on Xbox 360, PS3, PC, Wii U, and PSP.