This feels like a distinction without a difference. Would you say a Python script/Java utility doesn't "run on Linux" because you need Python/Java installed?

Programs running under wine don't have the same level of system/desktop integration as native programs, it's a very important distinction.

You still haven't explained how this is different from Python or Java applications.

Semantically you wouldn't, because they require their specific run-times. The difference is that those run-times are built to work natively on Linux (and often are enmeshed within its distributions), whereas any software requiring WINE is built to natively work on Windows, but is able to be translated for Linux. That distinction, between a native built runtime and a translation layer, is pretty major, and I think is why you can argue the colloquial usage of the term 'runs on Linux' differs between the two.