That's just a bad name. This is essentially a nonrandomized unblinded controlled trial using representative sampling. Only two steps below a full RCT unless you suspect foul play.
I'm not sure how you'd blind lack of sleep and that's not the point, so the only issue is lack of randomization.
Quasi-experiment is not necessarily a bad thing. It is to denote a study that does not have a traditional control-experiment structure with explicit pre- and post-measurements. This is particularly difficult to do with real time data analysis over time periods or with concepts that have ill-defined units of measurement.
For example, productivity and learning would be considered ill-defined. How can you prove more sleep makes you more productive? Since that is difficult, you can instead do a quasi-experiment or case study to observe the effects.
