The walking protagonist is most commonly found in games which place a large emphasis on their story and/or their environment. Though the character may walk as a default, usually there is a run button which makes the character move at a pace quicker than walking.
A character may move at a walking pace for gameplay reasons. Games with tight corridors and settings, which are in a realistic proportion to the protagonist, benefit from having the character walk through them. This increases the immersion as the protagonist (who tends to be human) is behaving more like a human would. Also, the character would probably not be able to jog or run through these environments without bumping into walls and other geometry, so walking allows the player to keep the illusion of realism by avoiding this.
Walking can also be seen as a way to define the character (i.e. Batman from Arkham Asylum). Walking can be seen to give an air of superiority. It shows a mastery of environment and that the protagonist is comfortable in a situation where others may not be. This device gives the player a sense of empowerment and, inevitably, they are having their ego satisfied by this.
The environment also benefits from a walking protagonist. The pace means that the environment is observed and spent more time in. Developers who wish to showcase their environments as having character
may choose to have their protagonist walk through them. This may also increase tension in an uncomfortable environment. Games such as Resident Evil have a creepy setting where a player is aware that they may receive a jump scare at any moment, but that anticipation is laboured and intensified by having the playable character move through the environment at a very slow pace.