Spent a few late nights, early mornings and lunch-breaks(!) completing my first game as India and, if nothing else, that 'one more turn' feeling was definitely there. Whilst, as most people are saying, there are lots of issues, I am confident they will be fixed in the near future when you consider how much Civ V improved over time.
I guess my main criticism would be about the lack of clarity ie. my lack of understanding of the game's rules. I was very excited about getting Civ VI so avoided all the previews and videos etc., so maybe that's the issue. But there seemed to be a lot of things where I just didn't get how they worked, and where there didn't seem to be any instructions—culture and tourism for example. It all felt very opaque—sometimes the numbers just didn't seem to add up. That's doesn't make the new ideas a bad thing—if they could be communicated better that should make things much more enjoyable. Furthermore, a lot of time was spent looking for things that were in Civ V—city connections, gold/science production, cargo ships, happiness, ideologies etc. So once I get my head around the changes, I guess things should be better in that way too.
A lot's been said in terms of the UI (lack of contrast on the map, missing shortcuts etc), so I won't mention them again. But the poor edge scrolling was a pain, and the way the mouse wheel doesn't zoom precisely where you're pointing was particularly annoying. At first I was worried I was missing important info which popped up, but the notifications ultimately seemed unnecessarily spammy—do I really need to know when another Civ has made a trade route? It would be good to map the units' colours to the leader's portraits at the top, as sometimes I didn't know who to click on. I'm not sure I liked the boosts—a lot of times they were happening accidentally, and Science seemed less 'vital' than before. I'm kind of mixed about the art style. Overall, I guess it's good to be different, and there are some beautiful touches such as the waves on the cliffs.
Similarly, the AI has been talked about a lot—it was certainly weird attacking Kongo with a fleet of bombers when all he had were a couple of club-weilding Warriors—so I won't repeat all that. However, what I would say is that it must have been difficult to code the AI if the game's rules were being altered and experimented with all the time during development. Now we have the vanilla release, that draws 'a line in the sand', where certain concepts that must have been quite fluid as the devs rushed to release, are now somewhat firmer, patches notwithstanding of course (none of us know the pressures from shareholders, management etc. that the devs must have been under, nor how often or significantly things changed as deadlines loomed ominously—how could you do the AI if you didn't have the rulebook?)
Essentially, whilst the game was engrossing, it wasn't compelling or immersive. As it is now, the AI's behaviour meant I was questioning things, rather than reacting to them within the actual game and trying to adapt my play appropriately. Thus, without any believable influence from the other Civs, it all got a bit mechanical and—dare I say it—boring. As others have said, the balance and pacing aren't quite there (but again I'm optimistic that'll be sorted), and I confess I've only done one full play-through on one map with one Civ—so, my experience is pretty limited. But, in conclusion my initial thoughts are these...
I liked it and enjoyed it overall. I'm grateful we have a Civ VI, that it is a 'pure' PC game, and that it hasn't been messed with in the same kind of way that happened to the once-mighty Sim City. It looks great by and large, and Firaxis have tried to do a lot of things where I think you can see what they're aiming for, and the degree of quality they're aspiring towards. Compared to my memories of how buggy and underwhelming Civ V was, I think the new game is a much better start, a great platform—one which I hope (and believe) will be built on to deliver the magnificent Civ VI game which at the moment seems to be so tantalisingly just out of reach.