What we have here is an old-fashioned, IGOUGO, hex and counter, terrain modifier, odds-based wargame. While it was originally built for iOS devices, it feels like it could have been taken from a 1970s-era Avalon Hill catalog. The very few concessions to modern sensibilities (and the computer) include fog of war and diceless random number generation. It's a no-frills game that somehow kept me engaged for an evening without noticing the time fly by.
Most of the eight campaigns have a dozen missions with (as far as I can tell) unique maps. It's pretty clear the maps are assembled from tiles with different terrain features. Even so, they look attractive and there are enough variations in tree tiles to prevent visual boredom. The units, especially tanks, are nicely modeled. As they wait to be moved, infantry looks around and tank turrets rotate from time to time. When you move them, tanks leave tread-marks that fade after a few seconds. It might be a simple game, but its developers put a lot of effort into the little details that can make a big difference.
A few holdovers from the mobile game exist. For instance, the menus are giant boxes with indistinct lettering. It's entirely playable with just the mouse, which has some advantages. One mode is hotseat multiplayer. Unfortunately, there's no screen between the end of one player's turn and the start of the next, so you get a quick look at the opponent's order of battle. On a smaller device, I suspect this is mitigated by handing over your phone while pressing the end of turn button. I don't intend to play multiplayer in any case, but it's awkward if you are thinking about it.
As befits the title, the battles involve German and American hardware from 1944. Since German tanks were more capable during that timeframe, the default game levels their abilities a bit to make more even matches. There's also an optional "Historical Mode" that restores the disparity and makes American missions harder. Another difficulty setting controls the behavior of the AI to make it less reckless. Reinforcements come at a fixed schedule and as you take victory points. Unfortunately, no units are carried over to the next mission so the only advantage to playing well is whether you get one, two or three medals.
Campaign progression is simple: complete a mission to unlock the next one. Battles don't seem particularly tied to real conflicts. The descriptions tend to be functional: take this victory point, reinforcements on turn 8, watch out for German Tiger tanks!, and so on. It's a little disappointing given the existence of the Panzer General series and the modernized Panzer Corps. Even so, Tank Battle: 1944 a no-overhead game with surprising staying power.