Instead of shotgun, the machine gun (originally found in the 2nd mission of the first campaign) is way better
It is, but I ran out of ammo quickly against huge numbers of enemies that each took a bunch of hits before dying (although maybe I had extra clips and didn't realize I had to manually reload). My comment about the shotgun was mainly that it's weaker than shotguns in most games.
Requiring the players to find secrets is an interesting idea. In theory, that sounds fine except that you have to make sure players know how the game works before you slaughter them for not knowing the mechanics.
Anyway, I watched the first video and it made it pretty clear that the game doesn't do a good job of showing players how things work. You have to realize that a new player doesn't know everything that you do as the developer of the game.
We don't necessarily know which flat-ish rectangles are switches and which are not (Most of them don't appear to do anything at all). We probably don't know that crates are breakable if they don't react to being hit multiple times (with sound and a visual effect of some kind, like particles or cracks appearing). I actually briefly tried breaking things the first time I played, but it did nothing so I moved on.
Players really shouldn't have to watch videos in order to know these things. The game should make it all fairly clear in some way. Switches could stand out more and maybe be a different color. Pieces of crates could break off when they're hit. Locked and unlocked doors could look different from one another. Walls that are destroyed could look different from walls that are not. The HUD could make it clearer that one number is the number of extra ammo clips you have (maybe using an icon of some sort).
I may sound like I'm being negative, but I'm not saying your game is terrible or anything, just that it feels like it's unclear/unintuitive for new players. It looks like it might be pretty fun after you know how everything works. There are a lot of small things that you can do to make new players understand how the game works without resorting to asking them to watch walkthroughs.