Opponent has a Nykthos, Shrine to Nyx. What man can my Fellwar stone produce?

Relevant rule:
106.7 Some abilities produce mana based on the type of mana another permanent or permanents “could produce.” The type of mana a permanent could produce at any time includes any type of mana that an ability of that permanent would produce if the ability were to resolve at that time, taking into account any applicable replacement effects in any possible order. Ignore whether any costs of the ability could or could not be paid. If that permanent wouldn’t produce any mana under these conditions, or no type of mana can be defined this way, there’s no type of mana it could produce.

I interpret this as follows:
“if this cards ability resolves right now, what colors could it produce?”. I.e. only the part after the colon is interesting. Which means that the opponent needs to have devotion for the color I am interested in. Is this correct?

Yes, that's correct. If the only land your opponent controls is Nykthos, Shrine to Nyx, your Fellwar Stone can produce only colors that your opponent has at least some devotion to. If your opponent has 0 devotion to a particular color, Nykthos currently cannot produce that color of mana, so your Stone will therefore not be able to produce that color.