Why the past tense? How do classical (or rather, orchestral) composers write music? How does any composer write music for instruments they don't themselves play?
Although a composer doesn't necessarily need to be able to play an instrument to a high standard, they do need to understand the mechanics of the instrument, its limitations and capabilities. This isn't really a matter of genius, just of study and knowledge.
It's certainly not "intuitive" - it's learned.
Composers tend to collaborate with musicians and make changes based on their input. So, for example, they might give a score to a soloist, have them spend some time with it, then come back with feedback - "this part is impossible to play, how about we change it like this."
Nowadays composers can, if they wish, try multi-instrument arrangements out on a sequencer. It's still useful to be able to imagine how an arrangement would sound, and of course in the past that was the only way.
The archetypal composer sits at their piano; a very useful tool for trying out harmonies etc.
It would also make a great deal of sense to write mini-arrangements before expanding them to full orchestral arrangements. For example, score a segment of your symphony for a string quartet, and have a string quartet play it for you, as a prototype for the final work.