I think that’s a real possibility. These bottles are a bit of a static magic trick, and misdirection—artful lying—is the coin of the realm in magic.
The video clearly shows a molded-in “20 CL” at the base. That’s 200 ml, obviously. The first thing I’d do is immerse the bottle in water up to a likely fill point and measure the displacement.
I’d use that displacement value and a SWAG at wall thickness (plus the known density of likely glasses) to see if we were anywhere near the right volume. While that probably wouldn’t yield a “eureka” moment, it might tell us whether the bottle was previously cylindrical.
I’d also look at all the 20-cl bottles available in Europe to see if any have similar or identical molded bases. That may be a needle/haystack problem, but the bottle’s shape is odd. Besides, sometimes you get lucky.
Someone mentioned distortion about halfway up the bottle. I see it too. I’d look at the bottle through a polarizing filter to check for photoelastic discontinuities—those would strongly suggest pressing. Here’s what I mean:
I also think that rolling individual cards through the wide mouth is plausible. One could minimize distortion in the assembled deck by alternating the rolling direction successively between concave-face and concave-back.
I think the cork is more aesthetically pleasing than a generic metal cap, so maybe that’s why he uses corks. But I bet he’d use white wine bottles if he could. That seems even more marketable and lends a little credence to the rolled-card theory.
None of these ideas is a slam-dunk test, but they could collectively point in the direction of another test. But I bet the bottles are altered as Chronos and others suggest, mostly because:
The fabricator, Clifford Stoll, makes pseudo-Klein bottles too.
Occam’s razor suggests that an artisan skilled in glassblowing and related techniques would tend to apply those skills to a project like this.