The only "ramped-up 'silliness'" I've seen mentioned are the two natural wonders and the GDR. I'll freely admit that I'm not a fan of El Dorado and FOY, but then again they only appear in about 10% of the games. GDR is no more "silly" than Alpha Centauri ship, "Cure for Cancer,"
I have to nip it right there.
First, getting randomly punched in the face by a stranger is no more tolerable due to how infrequent it happens. Having something you dislike happen is not made better by how often it does or doesn't happen. The thing is, I am not given the choice to not have these in my game ever. How many games they show up in is irrelevant. How many hours you put in a game only to find them and instantly hold contempt for the game is.
Second, cancer has treatments that sometimes cures it. While there may not be a magic "cure all" pill for all the types of cancer, cancer is currently a curable disease and the probability of recovery depends on the type, it's maturity, as well as your health conditions and medical history. In a way, a cure for cancer exists. That is why a doctor sticks his finger in you butt when you turn 35. You want a good chance of being cured? Get examined.
Third, Alpha Centauri is a victory condition for a technological victory. It could be replaced by the Apollo moon landing or something. But again, here recently they announced the space station so it could just be seen as a representation for sustaining life off the Earth. The point is, it is a technological victory condition (parameter) and it is loosely represents something real.
Giant Death Robots has NOTHING close to real to be based on. Same goes for the two wonders. Imagine two movies came out this year. One looks similar to the new Total Recall (or Minority Report) and the other is more along the lines of 24 but is centered around cybernetic implants being tested on humans. Both are set in 2017. You don't think the Total recall one seems a bit more silly than the other. It involves major growth in economy, infrastructure, manpower or population, and technology in the ridiculous time of 5 years. The other, just technology.
planets shaped like a doughnut, etc. And of course Elvis and friends have been removed. Many non-serious "silly" gameplay features have been removed. No longer does "Leonardo's Workshop" instantly turn my warriors into Riflemen. Marco Polo (who may have never even been to China) no longer gives me intimate knowledge of every nation on Earth. I do not institute a modern Democracy in ancient ages because I made a pyramid some time BCE. I'm sure there are more (those are off of the top of my head and obviously my mind was going down the wonder track).
Got to snip it again. Remember I have played Civ since release night of Civ 1. I have a tolerance for silliness. I have no problem with these things.
Random Events--you say you didn't like them, and of course they've been removed. Are they more or less "silly" than a futuristic mech unit? What's the net "silliness" loss/gain there? Or are you just thinking about things added and not features removed?
Actually, I presented the idea of random events on this very forum and some of my examples were used in the game. I said some are broken and feel they were poorly implemented but I modded them how I wanted them. I'll pull up that thread when I get off work and post it. I thought it was pretty awesome of Firaxis.
EDIT:
Here it is. I don't like the idea of bugging the player to constantly rebuild improvements and stuff. I just wanted the to throw a semi-big decision your way and have everyone get one at the same time turn randomly shift momentum in no ones favor but just in general.
I would say they are less silly because the things they represent are less silly. If a random event was something silly like a soldier was bit by a radioactive spider and now ignores city defenses, it's the same. But none are. They deal in things like volcanos, flood, city activities, etc. (Real things) the balance issues are salt in the wound to these new additions.
Are you basing your opinion of the tone of the entire game largely on two rare features and one late-game unit?
I am basing my opinion of the entire game on the entire game. While I don't see the flavor text as encroaching on gameplay, it still adds to the total lulz tone of the game. It isn't 1 thing or 2 things, it's a bunch of things. I bring up GDR, FoY, and ED because they stand out as a new breed of silliness to the main game that should be easily recognizable to long time fans. Plus, the OP mentioned them and I fully agree with him.