Having such a powerful trade enterprise that my culture spreads throughout other empires
What's the difference between building a massive trade network and accumulating lots of cash? The former results in the latter.
Having such a powerful culture standing that other empire's populaces will not allow war with my empire without facing revolts
The culture system we have now is fairly simplistic and would need to be overhauled if this were to be anything more than "build X culture centers to obtain victory". Again, accumulate enough cash to build the things.
Forcing an adjacent empire into vassal state status
Alright, you have me here; this one isn't economic. That said, it's just a variant of military victories.
Wonder victories
Amounts to paying for the wonder and sitting on it until the timer expires. Effectively an economic win, no different than building a trade route and waiting for it to pay off.
Controling x/z amount of trade routes
Just a repeat of "trade enterprise"
Having diplomatic superiority over all other empires, this would most likely involve having an embassy on so many planets within an empire, having enough spies within other empires, having enough treaties etc
We don't yet know how the diplomatic system will work yet, so frankly I don't think any of us can comment on this.
The kinds of victory objectives I want to see (as discussed in the other thread) are things like "there can only be X", where you can set the number of winners that will be allowed and the game ends when that many players are left standing.