It doesn't say of the winner chooses etc?

Just like any other quest, winner chooses.

The winner of rumor or previous quest?

The winner of rumor or previous quest?

Rumor quests are still quests.

The winner of rumor or previous quest?

Rumor quests are still quests.

And if they are playing Hob?

Same thing. I just used examples from the shadow rune.

There are some quests, that say in reward section "if OL has won this quest, the next available quest is X". That would contradict your ruling.

Those victory conditions do not account for rumor quests. They say "X or Y may be chosen by the winner as the next quest." In reality, the rumor adds a third choice, so it is (where Z is an available rumor), "X, Y, or Z may be chosen by the winner as the next quest."

After the rumor quest, the winner of the rumor chooses the next quest as normal.

Also, on a more general note, quest text always takes precedence over general rules text. Now, it's irrelevant in this particular case, because as Zaltyre said, Rumor Cards simply add another choice that you may take, but even if the quest said that you must take a certain quest as your next quest, it wouldn't so much "contradict" what Zaltyre said as simply add a variable that cannot possibly be accounted for, because quest text can say absolutely anything and always be right - each quest text has to be looked at separately in how it doesn't (or how it does) conform to the general rules.