As a child my four and half foot yew bow with only 40 pound draw put arrows through targets. Mind you my target wasn't an official one, it was painted on the bottom of a drawer taken from a chest of drawers. Still, that was several millimetres of plywood. So I don't think I would have fancied being shot wearing linen armour!
Compound and longbows are both known for being able to pierce the armour of the time when linothorax might have been used. It was insanely stupid to test it with someone living inside it.
However, from what I can see from the video (there's a second or two at 2:16), they were using a modern recurve bow (usually less powerful than compound/longbow), the kind often used at school which tend to sit around 20-25 ft/lb.
And it very nearly pierced the armour under those conditions.
Fiberglass is my answer to the technology you'd use to make a name for yourself if you woke up in medieval times. I think it should be possible to manufacture using period equipment, and there are many uses that would be interesting to that time period.
What I'm wondering is what kind of bows did they use.
I remember from school shooting arrows at targets and then some kids bringing in compound hunting bows that put arrows right through the targets.