In the past, a turbocharged engine on a small hatchback pretty much automatically designated it as a hot hatch, because it would deliver substantially more power over the same car in a lower trim. Example: golf vs GTI where GTI is a hot hatch and the golf is not. Same with Mazda 3 vs. mazdaspeed3.
The same cannot be said about the Sonic, though. The addition of the 1.4t motor over the 1.8 didn't gain all that much power over the 1.8 and it wasn't the intention. While the 1.4 has potential to be on par with similar hot hatches like the Fiesta ST, we're comparing stock to stock.
The 1.4 motor was an option to provide greater fuel economy. Nothing more and nothing less. You could say that the Sonic RS is closer to being a hot hatch, because it has distinguishing external differences akin to those of other hot hatches (GTI vs. Golf again), however without a substantially better engine performance (stock) to it's base variant, it still isn't a hot hatch. It's really a compromise, if you will. This isn't a negative statement against the Sonic, however. The RS serves those buyers who would like a hot hatch but do not want to spend the money on one - the RS comes very close in the mind of many buyers.
Again, this isn't a slam on the buying demographic or the car, it's simply a clever way to market the car. This is partially why Sonic has been a success for Chevy - it's an economical way to get close to the hot hatch market.
Turbocharged motors as a whole have become cheaper to produce as they've found their way into mainstream cars. They have also become more reliable. As more stringent CAFE restrictions are looming, manufacturers have begun to implement smaller turbocharged motors instead of larger na motors to provide the power people want and raise the fleet fuel economy numbers the manufacturers need. Look at BMW - they introduced a 2.0t motor to their 3 series now. '14 or '15 Mustang will have a turbocharged motor as an option, which is allegedly going to slot between the 6 cyl and the 8 (closer to 6) in regards to power.
As we see, turbocharged motors are primarily implemented for their power and increased fuel economy when compared with larger na motors putting out similar power.