First, check out how far into the horn she has to sing. Granted, she doesn’t have a particularly loud voice, so she probably has to put her head farther in than, say, a gospel singer who has more projection.
Then, listen to how the resonance of the metal horn insinuates itself into the timbre of her voice. Basically, they’re recording her singing into a resonant can.
Finally, check out the second half of the second video where they play the cylinder itself. We get to hear her song with all the scratchy, hissy, warbling artifacts one would expect from the wax format.
But what we’re really treated to is an A/B test between a digital recording of Vega singing (albeit, one that was synchronized to video and data compressed when it was posted online) and the wax cylinder playback (similarly digitally recorded and compressed). Notice the frequency bandwidth reproduced from the cylinder, as well as signal versus noise. Will future generations similarly listen back to our data compressed recordings and marvel at how lo-fi the sound was in the early days of web delivery and satellite radio? You’re darn right they will.
In the last few decades, a number of artists have recorded to wax and transferred the results to digital for aesthetic reasons, such as They Might Be Giants.
However, one of my favorite artists working in this realm is London-based musician Aleks Kolkowsky, who regularly records musicians to wax cylinder. Have a look and listen to what he’s done at Phonographies.org.