You need to use the MultiStream option if you want to deal with concatenated gzip files.

use strict;
use warnings;

use IO::Compress::Gzip qw(gzip $GzipError) ;
use IO::Uncompress::Gunzip qw(gunzip $GunzipError) ;

my $gzipped;
for my $txt ( qw(Alpha Beta Gamma)) {
    gzip \$txt => \$gzipped, Append => 1 
        or die "gzip failed: $GzipError\n";
}

my $out;
gunzip \$gzipped => \$out, 
        MultiStream => 1 
    or die "gunzip failed: $GunzipError\n";

print "Uncompressed is:\n$out\n";
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