Earlier quoted context omitted.
Would such a license fall under the definition of free software? Difficult to say. Counter-proposition: a license which permits training if the model is fully open.
It isn't the difficult, a license that forbids how the program is used is a non-free software license. "The freedom to run the program as you wish, for any purpose (freedom 0)."
You are still free to train on the licensed work, BUT you must meet the requirements (just like the GPL), which would include making the model open source/weight.