See, when I saw "Modern Retro", I thought about games that had retro elements in the story, not the actual gameplay... whoops.
Going with this different idea, I first thought of Bioshock. I absolutely loved all the Art Deco architecture, and even the guns were retro, like the Tommy Gun-style machine gun.

I found that Penny Arcade OTRSPOD had a great retro feel while also including modern ideals such as real time events and mini games.

Gravitron 2:
http://xout.blackened-interactive.com/Gravitron2.html
Simply the finest Thrust-ish game I've ever had the pleasure of playing. And not only is it AWESOME, but it's a mere $5 to buy. Highly recommended.
If you're used to such games, you'll find that G2 starts out really easy, but don't worry -- there is plenty of challenge in the later levels. And if that thought scares you because you already found it hard, then note that the author is also working on implementing a range of difficulty levels for one of the next updates, so before too long the game should cater nicely to most people :)

As far as GoG games, Kingpin did something similar. It takes place in a sort of alternate universe where modern and early-twentieth-century gangster culture are mixed.
The Ship could sort of count since, while ostensibly taking place in the 20s, there are little anachronisms everywhere, like ATMs and surveillance cameras.

When I see this topic, I think of ainc games, especially Tsunami 2010 (just look at the pictures and the download size!). Then there's also Echoes is basically a pimped version of Asteroids, a very enjoyable one at that.

When I clicked the Iji link, it took me to La Mulana. Just a heads up.
Edit: You made a mistake with the URL code. I fixed it in the quote