You can definitely see what MachineGames went for when making this game. It is a love letter to classical shooters in general, and the Wolfenstein franchise’s legacy specifically.
One of the places where this is evident is in its level design. Even if they are technically linear, they offer great room for exploration, alternative paths to completion (though not to the extent of say Deus Ex), and plenty of secrets and hidden supplies.
The latter point is what harkens most back to the classical shooters era. Games like Wolfenstein 3D, Duke Nukem, or Doom had the player relying on thorough exploration and observation to obtain the health and ammo necessary for survival, which required taking intricate paths through the carefully designed levels. One of the reasons modern shooters adopted a regenerative health model was to simplify that level design, and concentrate on spectacular set pieces. The New Order uses a hybrid system where the player will regenerate a little health (up to 20 points) but healing back to full strength requires you to scavenge for medikits in dark corners, or slice open metal crates with your laser cutter. (Oh and speaking of Wolfenstein 3D, sleep on the dirty mattress at the top of your hideout in the game, I dare you.)
Moreover some of the best weapon upgrades are completely optional and require you to actively seek them out. You WILL miss some stuff on your first playthrough. The levels also hide collectibles including Enigma codes that, pieced together, unlock special gameplay modes. All these together add greatly to the game’s replayability.
The weapons are decently varied and versatile, all of them using quite diverse alternate fire modes (seemingly in homage to Painkiller). In addition, all of them can be dual-wielded, from knives to automatic shotguns, allowing for many satisfying ways to vaporize Nazis.
There’s also a stealth system involved, though that’s pretty basic. It boils down to sneaking up behind troops and performing knife kills, or picking them off from afar with thrown knives or silenced pistols. There are also Commander-enemies on some maps that must be taken out, preferably quietly, lest they call for reinforcements. You cannot move bodies or anything of the sort, but it doesn’t matter because enemies don’t react to the sight of fallen comrades.
One more point of note for the game is the perk system. Persistent character upgrades like ammo capacity or speed with dismounted turret weapons and such can be acquired by performing a set of tasks, in a manner similar to achievements, though I must give the game praise for integrating it quite intelligently into the core gameplay, not making it feel artificial and disconnected like achievements usually are.