Because that made sense. He wasn't going to catch first place if she got it right and bet correctly. He was guarding against 3rd place being able to overtake him.

J! Archive has a "wager suggestion" for each Final Jeopardy based on the scores going into it. Here's what it says for this one:

"Jay: There's no way you can cover a rational wager by James, but if James decides for some reason to wager everything, you can eke out a win on a Triple Stumper if you wager no more than $4,600.

James: Try wagering $1,399, which is as much as you can put up against Emma without being usurped by a doubled score on the part of Jay.

Emma: Wager $20,201 to cover James."

And the bets were:
$6,000
$1,399
$20,201

So he did exactly what you'd expect in that situation. And so did the person in first. If he'd bet it all he'd have finished $1 shy of first.

[Post edited by AbsolutVT03 at 06/03/2019 4:51PM]