Maybe they haven’t developed anything more advanced that your basic bulky volatile RAM 8-bit arcade machine. Multipurpose desktop computers are a pretty big jump from there, just wait until she discovers what the internet is

I’d be willing to hazard that it’s some kind of difference engine, as designed by Charles Babbage in the early Victorian Era. His contemporary and friend, Ada Lovelace also managed to write a programming language for it. It was never used, as the design was implausible; specifically, it was done by clockwork rather than electricity, so the friction between the gears rendered it altogether a fire hazard. Also, something with the calculating power of, e.g., a good graphing calculator would have taken up a large room. However, Babbage and Lovelace did not have pony magic on their side. The idea of basic computation machines has been around for over a century our time. It’s not implausible that they may have successfully built and miniaturized a difference engine and simply failed to make the jump to electrical computing, thus explaining- or at least rationalizing- Twilight’s confusion.

Computers were around before arcade games. Even before console games. That said, maybe said computers weren’t around in the original universe but the alternate has what we use today. My opinion.

Logic. It was meant to be sent for the paper shredder.

Arcade machines =/= Desktop computers.

Who needs Logic?

@James Rye  
Perhaps this will answer your question:  
http://cheezburger.com/7727217152

@Background Pony #752F  
No.
 
Background ponies are exactly that: ponies in the background.
 
Fans do give some background ponies personalities, but not all of them. “Button” is one of those ponies.

@Background Pony #752F  
Look for yourself

@Background Pony #752F  
Did you not watch “Hearts and Hooves Day”? Image on the left is a screencap.

@Background Pony #752F  
That pic of him is from the show.

To be fair, Button Mash is a fan made character who isn’t canon. So in the actual show, Technology doesn’t really have great influence.

@James Rye  
Binary

@illuminati  
Even so, the idea applies. There’s no reason you couldn’t build one without lights.

@DrVillainous  
This one definetely has an electronic display, because you can see flashes of light on his face in that scene.

It’s possible that the “video game” in that episode was actually a machine along the lines of this. We could have built similar devices ourselves along with pinball machines long before computers if we’d thought of it.

Don’t even bother theorizing on it.  
This is also a place that has record players and film projectors, but has yet to master the concept of a ballpoint pen.

@James Rye  
Isn’t it three buttons? I’m thinking you use the two first buttons to select the letter and the bottom button to type.

@Background Pony #6D6E  
Shows up in the Hearts and Hooves episode, IIRC

@Background Pony Number 17
 
We have seen the ponies use those old writer machines though. THose with the two buttons. In the CMC episode where they got a newspaper and in the Daring Do episode. I still wonder what kinda letter system only uses two letters.

The authors just don’t give a fuck.

What’s that? It’s a show about ponies.

Actually, wait.  
You can have a video game that only uses two buttons.  
But you can not have a word processor or anything like that, right?

They are all playing Space Invaders or Pong.