Does Shadowrun Returns have random runs like Genesis's Shadowrun had?

No, I have played through the game and did not find any indication of random runs. I think this is to keep the difficulty throughout the game consistent without forcing the player to grind for Karma.

No there are no random runs. However, there are several DLC stuff (third party) you can download off of Steam Workshop that have random runs built in. Several of them are pretty open ended. Also there is a chance the new Berlin expansion will have random runs. So far that is one of the most important things missing from the game. Since the game is Modular I expect the developer to release many mods, plus many user mods to get released...so if there is nothing out there yet, there definitely will be. There was a user remake of the original Shadowrun that is going pretty well, it will definitely have some in it, if it doesn't already.