If you look at the sample, the exec method is called on a $chan object. And if you look at the previous line:

      my $chan = $ssh2->channel();
      $chan->exec('program');
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You'll see that is create using the channel() method. Look down for the documentation on the channel method and you find:

channel ( [type, [window size, [packet size]]] )

Creates and returns a new channel object. See Net::SSH2::Channel.
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That reference to Net::SSH2::Channel is a live link, and if you click it, you'll find:

exec ( command ) Execute the command on the remote host (calls process("exec", command)). Note that the given command is parsed by the remote shell; it should be properly quoted, specially when passing data from untrusted sources.

Modules by this author are better (if sometimes more tersely) documented than most.