You can see in your own video how.
He's not being captured. Effectively, the battle is lost due to Tywin Lannister's arrival with the House Tyrell and his own men drag him away from the battle.
To quote from the relevant section in the book:
Bronn smiled thinly. "From the winch towers, all we saw was banners in
the mud and men throwing down their spears to run, but there's
hundreds in the pot shops and brothels who'll tell you how they saw
Lord Renly kill this one or that one. Most of Stannis's host had been
Renly's to start, and they went right back over at the sight of him in
that shiny green armor."
After all his planning, after the sortie and the bridge of ships,
after getting his face slashed in two, Tyrion had been eclipsed by a
dead man. If indeed Renly is dead. Something else he would need to
look into. "How did Stannis escape?"
"His Lyseni kept their galleys out in the bay, beyond your chain. When
the battle turned bad, they put in along the bay shore and took off as
many as they could. Men were killing each other to get aboard, toward
A Storm of Swords - Chapter 4 (Tyrion)