Something like this? Only handles a single request at a time, though.

#!/usr/bin/perl

use strict; # https://perlmonks.org/?node_id=11134663
use warnings;
use IO::Socket;
use IO::Select;

my $listen = IO::Socket::INET->new( LocalPort => 8080, # setup
  Listen => 256, Reuse => 1) or die $@;
my $sel = IO::Select->new($listen);

sub checkforrequests
  {
  for my $fh ( $sel->can_read(0) ) # 0 for poll
    {
    my $socket = $fh->accept;
    my $request = '';
    1 while sysread $socket, $request, 4096, length $request
      and not $request =~ /\n\r?\n/; # empty line test
    print $request =~ s/^/got HTTP packet: /gmr; # FIXME for testing
    # FIXME process request here
    print $socket "OK\n"; # FIXME sample response
    $request =~ /quit/ and die "exiting on 'quit'\n"; # FIXME for test
+ing
    }
  }

while( 1 ) # your loop as I understand it
  {
  select undef, undef, undef, 0.2; # FIXME your non-network stuff
  checkforrequests(); # this is added to your loop
  }
[download]

I used wget to talk to it, like this

wget -q -O - http://localhost:8080/CMD=changeplaylist
[download]

and I get an output of

got HTTP packet: GET /CMD=changeplaylist HTTP/1.1
got HTTP packet: User-Agent: Wget/1.21.1
got HTTP packet: Accept: */*
got HTTP packet: Accept-Encoding: identity
got HTTP packet: Host: localhost:8080
got HTTP packet: Connection: Keep-Alive
got HTTP packet:
[download]

A clever client could hang it if it tried. Should probably be done with a more extensive multi-connection handler, but they get bigger :)
( Which is why monks, including me, will suggest using an async package.)