Well, apparently it's now been moved into the category of "undocumented feature", meaning they're not going to fix it most likely. But yes, it's a bug, something we've known about for a LONG time.
Basically, what happens is this. When you pick a difficulty level, it loads a whole bunch of multipliers. Prince is the default, where everything costs the listed amounts. On Chieftain, buildings and units only cost ~80% of the normal amount, tech costs are reduced by about the same, and most importantly, unhappiness from city number and size are multiplied by 0.6. On higher difficulties the unhappiness stays at Prince level, but other factors come into play to make things more challenging. (AIs starting with extra techs, better growth bonuses, and so on.)
The problem is that while you're on Prince, the AI seems to default to Chieftain, and is getting many of the bonuses intended for unskilled players. (There are SOME AI bonuses that tie to the difficulty level you choose for yourself, though, so it's not an across-the-board thing.) So while you're generating 3 + 1/pop unhappiness for your cities, the AI is generating only 1.8 + 0.6/pop. AND his cities are growing more quickly than yours, because the amount of food needed to grow is being reduced a bit. This basically makes up for the AI's inherent inefficiency; it won't connect resources as optimally as you would, it won't build buildings in the best sequence, and so on. But it's not really done in a coherent way, and this Happiness issue is just the most obvious result. More Happiness means more Golden Ages means much more gold for the AI players...
So you can change this in a mod. Just change the AI's default difficulty to Prince, and suddenly it'll be on the same Happiness curve as the human player, along with the research speed, growth rates, etc. This'd make the game much easier for you, assuming that you didn't change anything else to compensate. (Which is why in my mod, I've changed a bunch of other things to make it harder for the player to gain a significant advantage.)
