doubling back on me <like that>

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Senior Member
In the animation ''Mr. Peabody & Sherman'', Mr. Peabody (a dog) and his adopted son (Sherman) are running away. The people who are chasing them find them and the ensuing conversation goes on:
Man: I've got you now.
Peabody: Indeed you have, Monsieur Robespierre. And what a master of the chase you are.
Man: Oh, you noticed?
Peabody: Of course. Doubling back on me like that. That was genius.
Man: Thank you.

I don't get the meaning of ''like that''. I would appreciate it if you rephrased the whole sentence.
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