Might as well get more specific with evil-compatible 4X titles beyond Civilization:
Galactic Civilizations II has good, evil, and neutral-leaning races, as well as a morality system consisting primarily of random events which can be responded to in one of three alignment-matching ways. Fascinatingly, the good options often have genuine costs and the evil options typically have tangible benefits, which I thought adds a nice layer of gravity to the choices, as opposed to just asking you which colors you'd prefer to wear.
Endless Legend also has a variety of races, but goes a bit deeper with the ravening horrors category. One race is an ever-hungry swarm of plague bugs, another is a cult seeking to subjugate everything and destroy the legacy of the masters that abandoned them. There's also independent villages to raze, bribe, or convince, and on the former plus rebuilding or either of the latter two, become subservient to your empire.
As another point for evil, and better yet the quality of the game itself, the races really do play totally differently. Pretty sure the swarm has some kind of cannibal tech for sacrificing population to increase food production and happiness, and they literally cannot be at peace with anyone (Cold War, ie staring at each other warily, is fine). They also suffer food penalties, in line with their endless hunger, and so have to... compensate, somehow. The cult, meanwhile, cannot found or conquer cities, and has to spread by converting independent villages (and, should they find themselves at war, can only respond territory-wise with scorched earth).
Alpha Centauri is ancient, famous, and technically of Civilization lineage, so I probably don't need to mention it, but I feel it's worth special mention because of the depth of the heinous things you can do. You can implement various social policies/priorities, some of which are of dubious morality (Police State and Fundamentalism come to mind). You can utilize the local alien wildlife against enemies, which are stated to fight by instilling paralyzing terror and then burrowing into their skulls to lay eggs. You can of course raze cities, there's a module to equip your units with nerve gas (+25% Attack Bonus! Woooo!), and the ultimate weapon of the future, planet busters, severely deform the terrain where they strike, making it possible to bury enemy cities in the sea. When that fails, of course, they still reduce population by half or something heinous like that. There's also some nasty probe team (black ops) options for population decrease and so forth, and terraforming lets you some insidious things (drying out downwind neighbors, gradually sinking terrain into the sea) if you're patient and can get near their territory. Oh, and when your people riot? There's an option to "nerve staple" them in order to get things in line for a bit.
As a cherry to all of this, you have a reputation based on a combination of this and breaking treaties, so it's not like other leaders won't acknowledge when you exterminate a city or deploy nerve gas against enemy forces. Alien worms to the skull does not, amusingly, appear to be covered by these UN conventions.
There's a lot of other games I could mention where you play as evil races or do evil things, but in a lot of cases it doesn't really show through, or shows through only occasionally. In Age of Wonders: Shadow Magic, for instance, you can play as dark elves, which are evil and unpleasant. In fact, they're so evil and unpleasant that they suffer a morale penalty when owned by or placed into the same army as good races, like halflings. Then there's the undead, who suffer from similar issues, but are so evil they also suffer penalties for having to deal with neutral beings, like humans. That's right, they're so evil they can't stand anything that isn't evil. On the action end, you can migrate the native race out of a city to make room for your chosen people, or raze it entirely. If you're a Death Mage with the right spell, you can even reanimate the ruins into a city of the dead afterwards.
Trouble being, other than that it's largely a matter of assumption. Are undead cities any worse to live in than goody-two-shoes elf cities? One would think so, but there's not a lot of evidence to support that notion; they both build the same buildings, have morale issues, and so on. The idea that exiling a city's population to make way for your own would be excessive is also be nice, but it's kind of a standard feature, not an evil-centric thing. Razing cities at least reduces your fame, but again, not especially good or evil. So... most of the evil in that game is a matter of background fluff or these occasional things you can do every now and then.
Actually, I'll give an honorable mention to Orcs Must Die! 2. I haven't played the first one, so I don't know how much explanation they gave in that one, but in this one you butcher wave after wave of orcs and related creatures because... er, well, because they're invading through the portals, presumably trying to get into your world where they'll... do bad things, presumably. And you need the portals open because that's where magic comes from, or something, so... long story short, the meat grinders are totally reasonable and justified.
So yeah, probably wouldn't make the list for a couple reasons, but has that common and amusing "wait, I'm a ruthless butcher" vibe to it, made all the more literal by the methods you tend to use.