"8-bit" or "New Aesthetic" games like Minecraft, Bit Trip Runner, and arguably Dwarf Fortress are increasingly popular, perhaps reflecting a newfound appreciation for gameplay in place of high production values. To some extent this is also a way to disguise lack of production values: if you put crappy models on top of Unreal Engine, the environment they're in makes them look worse by implicitly comparing them to the ones in Counterstrike or Call of Duty [0], and indie devs can avoid suffering such comparisons in part by avoiding the engines that create production-values expectations they will inevitably fail to meet.
[0]: CoD is on Unreal Engine, right? Did I misspell that?
Occasionally there are games programming competitions that focus on some kind of artificial restriction like this, sometimes even using specific old platforms. The problem is that, for obvious reasons, these restrictions tend to resemble restrictions we have actually suffered in the past, so the aesthetic of the games tends to be somewhat predictable: square pixels, small color palettes, 2.5D, 7-segment displays, FM or square-wave or triangle-wave synthesis.
But what if, instead of creating video games that recall the age of Space Invaders, we tried to create video games that recalled the analogous stage of technological development on an alien planet, or perhaps an alternate-history Earth? We could have been laboring under different restrictions and produced different kinds of games.
A number of things have happened recently in games that suggest some possibilities. Flappy Bird could easily have been written in 1985 [1], but there were no similar games. 3-D wireframe games were feasible in 1985 (Maze War, the first first-person shooter, was from the 1970s, and the Star Wars game was a popular arcade game of the time) but they greatly benefited from vector displays, which went out of style at the time.
[1] I think James Hague pointed this out but I'm offline at the moment.
So, some example alternative histories:
As I said, what if vector displays?
What if hexagonal pixels had been the standard? They have more consistent spacing and thus reduce sampling error for the same number of pixels, which is why tabletop strategy games (arguably including Settlers) use hexagonal tiles.
What if Tek-4014-style storage tubes had been the mainstream display technology? You can't erase part of the screen; you have to erase the whole screen.
What if touchscreens? But we're already exploring that with game dynamics like Flappy Bird and Angry Birds.
What if timesharing?
Music synthesis with electronic difference engines, sort of like vector-display display lists, but for waveforms?
a. Music synthesis with circulating bit sequences in shift registers (like the Apple ]['s NTSC colors) rather than analog waveforms?
Vector displays with higher-order display lists? You could display quadratic splines as easily as points, but maybe only a small number of new ones per second.
What if the CPU itself were fundamentally different in some way?
a. If most of your memory were write-once read-many, so that every time you played a game, you irreversibly used up some of the memory?
b. If most of your memory were fundamentally sequential-access, like bubble memory or magnetic tapes? (Arguably we're suffering that now with disks, and of course videodisc games of the 1980s explored some of this too.)
c. If the CPU were a combinator-graph reduction machine like the SKIM rather than a RAM machine?
Character-cell displays created an aesthetic that survives in Dwarf Fortress and Nethack, but also that influences any number of modern "8-bit" games, because they use fixed-width fonts. But to a great extent those displays were very culturally contingent, and while perhaps Greek and Latin alphabets are among the simplest systems to draw this way, it seems like it's probably a coincidence that the cultures that invented computers happened to use alphabets rather than other writing systems. So consider, what if your character display were for a language that was:
a. Top-to-bottom?
b. A syllable-block system like Korean hangul?
c. One of those where accents are essential to understandability? Maybe, like APL, your display would need to support arbitrary overstrikes, or at least two or three overstruck characters. How could this reduce the size of the character set?
d. Necessarily variable-width, or necessarily supported character overlaps? I don't know if Devanagari, for example, is actually this way, but I've never seen non-proportional Devanagari. Proportional font rendering isn't actually that much harder than fixed-width font rendering. Historically it came along with framebuffers, which certainly make it easier, but are framebuffers really necessary?
e. Ideographic? Would you necessarily move to a small syllabary for computers, like 1980s Japanese PCs used katakana, or could you perhaps handle some kind of large ideographic character set in reasonably simple hardware?
Hardware sprites and hardware scrolling were a big deal in 1980s games, since you didn't have time to redraw the entire screen each frame. Similarly, for fractals, hardware palette color-cycling was a big deal, a technique which also permits fade-to-black, flashing a certain color index, and so on, without having to redraw the entire screen; and a bit earlier, XORing objects into the framebuffer allowed you to move them around the screen without having to save the background they passed over in separate memory. But suppose the available display hardware had supported other interesting operations instead? Of course, there's an infinite variety of possible operations, most of which (like XOR) are mostly visually uninteresting. But there are a wide variety that seem like they would have been interesting but were never implemented in hardware:
a. Displacement mapping, which is kind of a generalization of sprites: you have a number that you add to the pixel coordinates generated by the hardware counter to get the address in the framebuffer (or tiles, or whatever) to draw the pixel.