my @maps_$game = HLDS::GameMaps("$game");

You already were told that it's a bad idea to use a variable as a variable name. In this case it's better to use a hash:

my @games=qw( cstrike dod czero gearbox ricochet dmc tfc valve );

my %maps;
foreach my $game (@games) {
        $maps{$game} = HLDS::GameMaps("$game");
}

## Visualize the data structure
use Data::Dumper; print Dumper \%maps;
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So that has created a hash named %maps, storing the arrays returned by my subroutine? My sub returns an array named @maps regardless of the arg passed to it, does create a conflict? How do I access these arrays that are stored within a hash?

It should have been $maps{$game} = [ HLDS::GameMaps("$game") ]; (Note the square brackets). The square brackets create an array from the list returned by GameMaps, and returns a reference to that array. The reference is then stored in the hash. @{$maps{$game}} is the array of maps for game $game.