No. I copied and pasted that. The definition says 'the Sun'. There was a proposal to classify 'exoplanets' but the IAU never accepted it, and so those large masses orbiting other stars remain undefined.

Exoplanets are addressed in a 2003 position statement issued by a now-defunct IAU Working Group on Extrasolar Planets. However, this position statement was never proposed as an official IAU resolution and was never voted on by IAU members.