Well, it is doing what you told it to. This rule

    section: server | key
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says you have section which have either a server or a key and no more. So it stops as soon as it parses one of these. If you exchange the order of the lines, as in:

print Dumper $parse->section ('
    tsig-key "/etc/bind/rndc.key"
    bind-server 127.0.0.1
');
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you're gonna see it parses the tsig-key line correctly but ignores the next one. You need something like that:

    section: (server | key)(s)
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with some extras to get the data structure you want.

Update: the real problem was spotted by davorg in Re: Parse::RecDescent trouble — $parse->section was being used instead of $parse->config. I've got confused by the rule name "section" to hold a single part ("key" or "server"). I expected a config to contain sections and sections to contain (possibly) multiple parts ("key" or "server").