They are statistics insofar they are calculated from samples, but that term is too broad to be a good answer.
The term goodness of fit is well established, except that some of those measures are inverse and really measure badness of fit, a term occasionally used, by J.B. Kruskal among others. But that objection is at most a quibble, and it's well understood in statistics, as elsewhere, that performance measures can be direct or inverse, so that usually people want high $R^2$ and low chi-square, or low inflation and high GDP growth, or whatever.
As another example, root mean square error should ideally be low, with nothing else said.
(If you know about overfitting, you'll know the limitations of these comments, but here the focus is on terminology.)
I like the term figures of merit, as an all-purpose term used in several fundamental and applied sciences. Again, merit can be direct (number of Nobel Prizes won) or inverse (number of downvotes on Cross Validated).
The term indicator is not especially good for your purpose and certainly not synonymous with goodness-of-fit measures. As @Tim explains in his answer, there is a much more specific technical sense, and as I emphasise in my comments on his answer, there is a much wider, less technical sense for the term indicator. There is no middle ground in which indicators mean goodness-of-fit statistics, exactly. But if you were to talk about goodness-of-fit indicators, I don't think you would be misunderstood. It's just not an especially good term for the purpose.