Getting out of bed is a muscle-building exercise for someone recovering from a coma. Tabatas and other High Intensity Interval Training, or jogging, or walking, or anything can build muscle, if the person doing it is unadapted to the activity. So yes, "cardio" exercise is an effective muscle builder, for a limited amount of time, in some circumstances.
When an untrained person starts an exercise program, they get stronger. They always do, no matter what the program is. This is because anything they do that is physically harder than what they’ve been doing constitutes a stress to which adaptation will occur. I’ve said before that for this rank a novice trainee, riding a bicycle will make his bench press increase – for a short time. This, of course, does not mean that cycling is a good program for the bench press for anybody. It just means that for an utterly unadapted person, the cycling served as an adaptive stimulus. A novice responds to each exposure to a stress the same way – he adapts. So each workout for a novice can be an adaptive stimulus. The problem with cycling for a novice bench-presser is that cycling rapidly loses its ability to act as an efficient-enough systemic stress that it would continue to drive improvement on the bench, since it does not produce a stress specific to the bench press.
You're new to the elliptical. It's different enough from your other training that it caused an adaptation, which may (or may not) involve muscle growth. That doesn't mean it will continue to do so.
There’s no link between muscle soreness and protein synthesis; no link between muscle soreness and long-term growth; and no link between muscle soreness and muscle fiber damage.
Muscle soreness happens when you create enough total damage to aggravate the connective tissues. This will sometimes correlate with a muscle-stimulating, growth-inducing workout. But just as often, it has nothing to do with muscle stimulation.
Just because you’re not sore doesn’t mean your muscles aren’t inflamed and growing. Likewise, sore muscles don’t mean you had a good workout.
DOMs can be used as a rough gauge of how well you're adapting to an exercise, but it's inexact and not particularly useful for gauging the long-term efficacy of a given exercise.
The write-up linked in the heading is good. Flann, LaStayo, McClain, Hazel and Lindstedt got similar results in an experiment:
Subjects were divided into two experimental populations: pre-trained (PT) and naive (NA). Demonstrable muscle damage was avoided in the PT group by a three-week gradual ‘ramp-up’ protocol. By contrast, the NA group was subjected to an initial damaging bout of exercise. Both groups participated in an eight-week high-force eccentric-cycle ergometry program (20 min, three times per week) designed to equate the total work done during training between the groups. The NA group experienced signs of damage, absent in the PT group, as indicated by greater than five times higher levels of plasma creatine kinase (CK) and self-reporting of initial perceived soreness and exertion, yet muscle size and strength gains were not different for the two groups. RT-PCR analysis revealed similar increases in levels of the growth factor IGF-1Ea mRNA in both groups. Likewise, the significant (P<0.01) increases in mean cross-sectional area (and total muscle volume) were equal in both groups. Finally, strength increases were identical for both groups (PT=25% and NA=26% improvement).