"... I didn't use export. ... Is that the same as export does?"

export is a shell command that adds a variable and its value to your environment; this will be picked up by subsequent processes. You'll probably have a lot of variables in your environment already. Try these:

$ env | sort | less

$ perl -E 'say for sort keys %ENV' | less
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Your author tests contain:

unless ( $ENV{RELEASE_TESTING} ) {
    plan( skip_all => "Author tests not required for installation" );
}
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`export RELEASE_TESTING=1` results in $ENV{RELEASE_TESTING} having a TRUE value: your author tests will now be run.

"I did it that way following the instructions in ..."

Step 6 has: "Now you run all your tests ...".

If you don't set RELEASE_TESTING to a TRUE value, all your tests will not be run.