Everybody's Gone to the Rapture developer, The Chinese Room, has addressed the issue about the lack of a run button.

In a blog post, the developer's creative director Dan Pinchbeck revealed that by holding down the R2 button, your character build up speed over a couple seconds. There is a reason for this however, as the feature was a late addition, which is why the game does not mention it. An automatic sprint feature was originally included, but was taken out due to playtesters wanting to have a choice.

“So together with Santa Monica, we made a late call. We replaced the autosprint with an R2 trigger hold, keeping the gentle ramp up to main speed.” Pinchbeck said. “This then needed testing, because it potentially threw out all of the pacing we’d been working on for the last year, plus could cause issues with accidentally parkouring into places you couldn’t escape from, creating game-breaking bugs. All this took time”

Everybody's Gone to the Rapture launched today on PlayStation 4 and so far, the game has been been met with positive reviews.