How long can polyethylene molecules be?
Short answer? Possibly, but these ones aren't.

So, the other thing mentioned in the video is that the specific material he's using has a molecular weight of approximately four million. If we assume it's ordinary poly-ethylene oxide, we can get the rough number of $\ce{(CH2)2O}$ subunits by just dividing by the molecular weight of the subunit:


$(12 \times 2) + (1 \times 2) + 16 = 42$
$\frac{4000000}{42} \approx 95000$


So, if we assume that each $\ce{C-O-C}$ back-bone unit is stretched out like a di-methyl ether molecule, a quick check on a fairly standard Ghemical force field gives me a subunit length of approximately 3.7 Å.


$3.7 \times 10^{-10} \times 95000 = 0.00003515 \text{m}$


So, these molecules should be about 0.04 millimetres long. Not exactly astronomical distances, but impressively long for a single molecule.

In theory, I don't think there's anything stopping you making a molecule as long as they claim, but these ones certainly aren't. I think also that the longest (synthetic) polymers in common use are of similar molecular weights and thus similar lengths: ultra-high molecular weight polyethene seems to top out around 4.5 million for commercial applications, from a quick search.

Biological molecules frequently get longer than this, though, especially DNA: the average human chromosome apparently contains a single DNA molecule approximately 5 centimetres long.

The man explaining in the video may have erroneously given the figure for the total length of all the molecules in that beaker.