"Why can't games just be fun anymore?" - Redundant Internet Dickhead.
This is near enough the quote I've read in numerous comments and forum posts across the web. Before GamerGate, before the Hitman: Absolution trailer, people (usually identifying as "gamers") have sought to trivialise gross sexism by pointing out that the transgression has occurred in a medium known for the frivolity of scoreboards, acrobatic plumbers, and any other number of tropes that are difficult to take seriously.
I start with this acknowledgement because apart from seriously questionable costume choices and historical sexism, Double Dragon Neon is a thoroughly enjoyable sidescrolling beat-'em up. If you can swallow the recycled damsel in distress pretext for the ensuing two and a half hours, and some super sexualised women combatants, you'll have fun.
The combat system uses the best parts of side scrolling brawlers and fighting games like Street Fighter Alpha 3. Traditional kicks and punches can be mixed up to wind opponents where you can then launch, juggle and throw. You can follow up with attacks on downed opponents, and even set up group attacks if you've managed to stun two enemies simultaneously. Rounding out the arsenal is super moves (which drain an energy bar), running attacks, and the ability to roll and duck to set up "Gleam": a status which grants a boost to your attack. The wealth of offensive options means that the action never gets stale.
Boss fights also allow for variation. Most involve pattern recognition so you can beat on big people and/or monsters without taking damage. One even incorporates platforming into the mix, and the result is stellar. There's a sense of humour to some of the enemy designs that's better executed here than in your average brawler.
Messing around with tapes was how I overcame the final fight. Equipping different tapes allows you to experiment with super moves and fighting styles, which in turn determine the amount of health you have, and your ability to take and deal damage. I'd played the entire game with "Training Wheels" on, but switching to an attack-heavy style meant I spent less time avoiding deadly attacks.
Double Dragon Neon is, on one hand, charming with its relatively-deep fighting system and its overt, eighties-flavoured sense of humour. This charm is then periodically dispelled by scantily-clad women begging "Punish me!" as they expire. There's a line between nostalgia and sexism that is carelessly walked here, but in the end, it's very easy to recommend provided you know what you'll find.