Output of i3 --moreversion 2>&- || i3 --version:

Binary i3 version:  4.13-non-git © 2009 Michael Stapelberg and contributors
Running i3 version: 4.13-non-git (pid 699)rl-c to abort…)
Loaded i3 config: /home/gandalf3/.config/i3/config (Last modified: Wed 12 Apr 2017 11:17:14 PM PDT, 220408 seconds ago)

The i3 binary you just called: /usr/bin/i3
The i3 binary you are running: i3

URL to a logfile as per http://i3wm.org/docs/debugging.html:

http://logs.i3wm.org/logs/5744863563743232.bz2

What I did:

Started peek and clicked on its click-through-able region during recording.

What I saw:

The click was received by peek and not the program underneath.
For what its worth, I observed the same behavior with licecap running in wine.

What I expected instead:

Mouse events to be received by the program under peek.

According the the peek developer, this is likely an upstream issue.