I'm going to fly in everyone's face here. :)
The art of prose writing does not consist merely in using stock phrases to describe new things, but in crafting new phrase and even new words, even if only to describe old things - and doing so in such a way that the meaning of the new phrase is immediately obvious.
I daresay the phrase "move out of a walk" is immediately, intuitively obvious to most native English speakers. It's actually very elegant. It is elegant and works because:
(1) It has analogs in our language that help make it intuitive, such as the aforementioned break into a run.
(2) Using a word like move, which is a fairly generic word, rather than break, which is somewhat more dynamic, helps to give a sense of lethargy. Even the word move is more given to being drawn out because all three of its phonemes m, oo, and v can be drawn out, whereas break sounds more decisive, more "snap" if you will, being bookended by b and k, which cannot be elongated but are very definitive, punctilious sounds.
(3) Being unable to "move out of" also gives a sense of being trapped, as the character no doubt felt.
I think the phrase a perfect turn of the English language, and fairly creative if the ngram is any indicator.
That all said, I can see how it might give a non-native speaker a hard time. It is unusual.