Artificial Intelligence (A.I.), is in the sense of gaming, used as a "third party" system by which governs everything in the game that it is programmed to. All AI systems are generally linked to manage several tasks, but certain cases (Yui for example) are tasked to handle singular tasks such as players' mental states and welfare.
Yui manipulating the system of SAO to summon a weapon.
Forms of AI can be set by other forms; not just programs. Such as:
NPC (Non-Playable Character): NPC's are types of simple/complex AI systems that are programmed into the world to appear as physical beings (shape of characters vary significantly), and can provide usable information. NPC's will not "react" to a player like another would in the sense that they are not supposed to have a chat with the player about how their day went so far.
Companions: This type of advanced AI system responds to a player and travels with them while providing support (health, ammunition, information, directions, etc...). Most of these companions can vary in appearance and forms; stats can also play a factor with how well the team works together and how responsive the system is to the player themselves.
Overall interaction with AI's are not generally possible to gain any sort of advantage over others in the game. AI's are simply there to assist and manage the game without any feelings or concern for the players. Yui's case, however, was different. Her job was to be concerned with the well-being of the players as their mental and welfare states were her responsibility. The AI system of SAO (The Cardinal System) is designed to specifically handle the data received by the actions performed throughout the game and any and all further data is stored. While true that AI's are not meant to change anything about the game to provide an advantage for others, it is not unheard of besides SAO.
A terminology to refer to AI's is "unforeseen miracles", by this term referring to that AI's are not seen, but do perform miracles in times of extreme crisis to prevent a devastating event from occurring. Most properties never dictate that an AI must listen to the system at performing its task. Yui sure didn't. Though her task was to manage the players' mental health, she performed other tasks such as trying to locate Asuna and Kirito in SAO. Under threat of deletion, AI's do not possess emotions and are basically programmed to do as they are told. As with any computer system, programs are only as effective as the people who made it in the first place.