I know this is the kind of question that could easily dismissed with a ‘No, it is not’. However, the Glossary section of the 2016/17 Laws of the Game reads that (link, p. 163):
The field of play does not include the goal nets, as defined in the laws of the game.
Law 1.2 states
The field of play must be rectangular
which is only possible if the area enclosed by the goal nets is excluded
And Law 1.12 states
No form of commercial advertising, whether real or virtual, is
permitted on the field of play, on the ground within the area
enclosed by the goal nets or the technical area…
which strongly suggests that the goal nets are not part of the field of play.
This would appear to be in contradiction with the glossary definition you quoted in the question.
I think it is reasonable to assume that the more detailed laws of the game have priority over a glossary, which gives a short and quick definition of various terms as an aid to understanding the laws.