Overlap between AI and "Game AI"
Nowadays, if you search for AI online, you will find a lot of material about machine learning, natural language processing, intelligent agents and neural networks. These are not the whole of AI by any means, expecially in a historical context, but they have recently been very successful, there is lots of published material about them.
Games, especially action games, tend not to use these new popular technologies because they have other priorities. However, under the broadest definitions, there is good overlap between AI in general and game AI, or more specifically enemy AI within a game:
Computer-controlled opponents within a game are effectively autonomous agents operating within an environment.
The game's purpose is to entertain the player, and this usually translates into requiring challenging and believable behaviour for actions taken by opponents (for some value of "believable").
A 3D map with a physics engine, other moving agents and possible hazards is a complex environment that needs some effort from a developer in order to define working behaviours.
Many games need to solve one or two classic AI problems such as pathfinding.
All the above means that the term "Game AI" is a good choice for describing how enemy agents are designed and implemented. However, there are large differences between goals of AI applied today in a 3D shooter and the goals of AI used in industry to control decision making.
Action games have a low CPU budget available per enemy for decision-making. Control systems in industry can have dedicated machinery, sometimes multiple machines, just to run the AI.
Action game priority is the game experience of the player, and this translates into strict targeting of a definition of "believable" for enemy behaviour that will entertain. In contrast, AI used in industry has accuracy as a high priority.
Typical game AI in 3D shooters
Developing enemy AI in games is a specialist skill, and only partly related to the purpose of this site. For detailed discussion you may want to look into Game Development Stack Exchange which has many questions and answers on topics like Enemy AI
Very roughly, the key traits of enemy AI in a game like Call of Duty could look like this (I have no inside knowledge of how COD does this, so may be inaccurate in places):
Enemies will have one or more modes of behaviour defined. This might be as simple as "Idle" and "Attack Player", or there could be many. For COD I would suspect there are many, and some may be in a hierarchy - e.g. there may be several sub-types of "Attack" behaviour depending on the enemy design.
Within a mode of behaviour, there may be a few different components defined, only some of which use AI routines. For instance, there will be specific animations related to walking or standing which are not AI, but there will also be some pathfinding AI if the agent is attempting to move around.
Decisions to switch between different modes of behaviour are often scripted with simple triggers, such as detecting player visibility using ray-casting between the location of player and enemy. When game AI fails to produce realistic results, it is often these high level triggers being brittle and not covering edge cases that causes it. Depending on complexity of the game and number of behaviours, there may be an algorithm managing the transitions between them, such as a finite state engine or behaviour trees.
Enemies will be presented with highly simplified observations of the game world from their perspective, in order to speed AI decisions.
AI systems will have CPU budget restricted. A 3D game spends significant resources rendering scenes, and will often try to render quickly, e.g. 100 times per second. There are multiple ways that AI budget can be allocated, but it is relatively common for AI calculations to be spread over muliple frames, and for search structures for tasks like path-finding to persist over time.
There will be a middle ground between scripted behaviour and AI-driven behaviour where analysis is done as part of game design. For instance, pathfinding routes may be pre-calculated to some degree. A system of way points is one example of this - it might be set by the game designer, it may be calculated by an AI component of the game asset-building pipeline, or it may be dynamically calculated and cached during a game session so that multiple enemy units can share it.
When complex AI is not needed to achieve a goal, when a simple caclulation or "puppet-like" behaviour would do just fine, then this could be chosen instead. For instance, an enemy "aiming" at a player can be a simple vector calculation, perhaps with a fudge factor of a miss chance depending on the range to make the enemy seem fallible and not as much like a machine.
I do not know how the behaviour of enemies using cover is implemented in COD. A simple variant would be to have each enemy hard-coded to use a specific piece of cover that usually works well against the player due to map design. However, it is definitley possible to have a search algorithm running (perhaps over multiple frames) that assesses nearby locations that the enemy could reach against the player's current position, and then pick those as variables to plug into the "take cover and fire on player" scripted behaviour. That assessment would use the same kind of visibilty detection between enemy and player that is used to trigger changes between "Idle" and "Attack" behaviours for the enemy.
As an aside, one related thing I find interesting is in using modern AI techniques to blend animations and make interactions between actors and the environment look more realistic. Although it is a lower-level feature than the question about enemy behaviour you are asking, it is an interesting cross-over between robotics and game playing that we will likely see in next-generation games, and probably applied first to the more detailed player model animations. Here is another example applied to a humanoid agent switching smoothly between different tasks, which any game player will recognise as something which game engines cannot do well at the moment - there are usually many jarring transitions caused by events in the game.
