Would run and gun games count? If so, I strongly recommend the Neo Geo Metal Slug games. They're all sold emulated on PC (GOG for the no launcher requirement).

And on a more usual sense of "shooter games", Saints Row The Third (GOG and Humble Bundle) and UNLOVED (original version is a mod of Doom II afaik). And just a note, Saints Rows The Third, from some tests I did a while back, seems to have a memory leak issue in character customization screens when running under default Wine.

Ravenfield for cartoony/low poly acradey fun

Operation Harsh Doorstop for something more like Project Reality

Good ol counter strike

If you are talking about multiplayer :

• The Finals
• Insurgency Sandstorm
• Hunt: Showdown 1896
• Hell Let Loose
• CS 2
• No More Room in Hell 1&2

Many options !