From my comment to the first guy:

They’re just shooters that are mechanically similar to old shooters like Quake and Doom, so you’re typically gonna have a mix of these traits:

• A wide range of weapons with unique uses (think rockets, railguns, shotguns, machine guns…)
• Chapters that you can complete in any order but the levels in them are completed linearly
• Colored keys to open colored doors
• A level-end screen when you reach the end of a level that tells you your completion time and what % of items/enemies are left
• And my favorite part, a lot of them have advanced movement techniques, which are usually identical to Quake (if not Quake 2/3) like bunnyhopping and rocket-jumping