I think you're using "flat" here to refer to an absence or rarity of fake 3D effects. Today's flat user interfaces go far beyond just eschewing those visual effects and remove almost all visual cues about what elements are interactive, what kind of interaction they support, what state they are currently in, and what the borders are between active and passive parts of the screen. Classic MacOS doesn't have those problems.
The screenshots you link to are flat in the sense of lacking 3D effects - I only see a single pixel wide dropshadow around windows. But they're not flat in the sense of being lifeless and unhelpful: There's clear highlighting of the active window and selected desktop item. The scrollbars in the first screenshot are not flat by nature, but flat because the content they enclose is currently entirely visible and consequently scrolling is disabled. The large blank spaces on the screen are accurately conveying what you can do to them (nothing), and they avoid cluttering the display to the point that everything else would need extra highlighting and color to be distinguishable as something that can be interacted with.
The screenshots you link to are flat in the sense of lacking 3D effects - I only see a single pixel wide dropshadow around windows. But they're not flat in the sense of being lifeless and unhelpful: There's clear highlighting of the active window and selected desktop item. The scrollbars in the first screenshot are not flat by nature, but flat because the content they enclose is currently entirely visible and consequently scrolling is disabled. The large blank spaces on the screen are accurately conveying what you can do to them (nothing), and they avoid cluttering the display to the point that everything else would need extra highlighting and color to be distinguishable as something that can be interacted with.