I would definitely create a sequel to Half Life, using the new Frostbite 3 Engine. I'd make it in 64-bits only for Linux and Windows.
Minimum requirements would be 8GB of RAM, and 12GB or more recommended. R9 280X minimum for GPU.
Textures, meshes and more would be changeable in the settings. Up to 4K or 8K textures.
Include mod support, do not include DRM support, include on Online Multiplayer mode, allow custom character creation, allow hosting servers (if the server passes minimum requirements on internet bandwidth, hardware, software, etc), multiple endings in Story Mode/Single Player (including more about the background story).
It would be full of easter eggs, and there would be several bits and pieces of text written "they said the number 3 - hl3 confirmed" in journals and on the walls, as a reference to internet rumors, among other things.
It would have full-blown OpenCL-accelerated Physics, customizable lighting (in-game support for ENB-like mods), Mantle support, etc.
It would include destructible objects (like Battlefield 4), Sandbox gameplay style, support for 4K resolutions (and beyond!), and include in-game Settings so high they wouldn't be playable for the next 2 years even at current resolutions.
The Settings would be automatic, and the gamer would have a slider for CPU, GPU, Resolution and other things. It would then automatically apply the settings without having to restart the game.
No loading screens. Immersive and customizable HUD. Adjustable Surround Sound support. Configurable AI, and support for OpenCL-accelerated AI.
I'd add weapon modification support, for things like scopes, laser sights, extra ammo, etc. I'd also allow the character to have a choice between 7 main playing styles (stealth-based attack and elusion, scenario-based strategy, offensive, defensive, dodge/deflect/reflect-based combat, non-combat-based effects, and lastly healing/regenerative-based support), where he could choose to use either one or more, but that would depend on the weapon, environment, opponent and more.
Difficult boss battles, hoard battles, hard-to-hit single opponents. Scary moments in the game. Make strategy important in the game.
Make killing monsters less of a grinding chore, and reward players for clearing places. Also reward exploration with lore knowledge, skills, items, and more. It makes the game more fun.
I'd also add multiple campaigns in the form of DLCs. They'd have the same amount of story and level content for single player, and add items to the main game, other DLCs and the multiplayer. It works like a content mod, except it isn't a continuation of the main storyline. It's a prequel, sequel, parallel storyline, or whatever else would most add to the game experience. It would be something the gamers could vote for within the game, but only players who bought the game with an official key could vote.
There would be support for MMO-like capabilities for those who want to do that kind of game mod, with support for skill trees, new levels, storylines, quests, new items and much more. This allows people to make an FPS game using this engine, RPG, RTS or anything else. Any modder could use this game engine's flexibility to make his own game on top, add or remove features.
Heck, make HL3 into a top-view 3rd person game like an RTS if you want. Make HL3 into an over-the-shoulder view if you'd prefer like other games if you prefer. Make HL3 into a medieval game in the world of Skyrim if you'd prefer. It's all up to the game modder, and players can download and apply these mods at will.
Also, include cloud-synced settings attached to the player's account, and include an in-game mod library support for players to preview game mods without applying them. Add mod tools galore using the in-game user interface, so that way it can all be done quickly and easily. Let the user save mod and game settings in the launch menu, so if something happens, the user can easily and quickly revert so his game doesn't brick on him. Also let a user save games with a list of mods he's running and his settings, and if/when he chooses to load let him choose whether or not to load the saved game file with it's saved mods and settings or to apply current mods and settings. (This lets avoid game crashes due to bad or conflicting mods.)