How close to a full release does it feel? It looks like a game I would only play once so I want that playthrough to be solid.
Not all that close. The most obvious example of it's early access state is on the main menu, where half the items are grayed out, including options. In the game itself, you get access to a ton of missions but so many are repeated (find 10 wool, go kill this bad guy, rescue 10 hostages, and rinse and repeat).
The gameplay itself is solid. It looks like Metal Slug, and the controls are similar, but it's a slower, at times more methodical approach than the frenzied style of it's spiritual predecessor. I found it nice that the bigger, more "badass" your weapon is the heavier it is and thus the slower you are. So there are moments, where you have to unequip the gun to allow yourself more speed and mobility to access certain areas. I'm halfway through the missions and only done it twice, though.
There are a bunch of glitches too. Any time I go to customize my weapon, the game will unequip my magazine. No idea why. So I have to make sure I go in and check that before loading a mission or I'll have one bullet per reload. And if that happens, you have to quit to the main menu. There's no easy way to go back to the home base, where you customize weapons, items, etc.
So the gameplay is fun, as it's a slower Metal Slug that feels almost like Mega Man; the guns are fun to customize, even though the system is buggy; the missions aren't varied enough; and the game is, quite literally, missing parts, like the options menu and small other things in various other menus.
I don't think it's worth $15 as it exists now. I was lucky enough to get it from Dunder for $7.50 and that seems more fair in it's pseudo-beta state. All this being said, I haven't tried anything but single-player, but if the people on the game's forums are to be believed it's way too easy on multi-player, as the game's difficulty doesn't scale well (or at all).