I have linked to Larousse, and Robert agrees that 'arrêter' can have intransitive use also. 

https://dictionnaire.lerobert.com/definition/arreter. 

Academie-francaise only lists 'arrêter' as transitive, but also notes  "arrêter de ...(faire qqc)" as correct use, so regardless of what definition of transitive/intransitive is used, the non-pronominal use of "arrêter de..(faire qqc)" is also correct. 

As noted, wordreference defines 'arrêter de (faire)' as a fixed verbal expression - locution verbale.

‘Arrêter’ can be transitive, or intransitive in some settings. (Larousse)

In this case,  ‘arrêter de faire’ qqc is a fixed verbal expression (wordreference).  

There does not appear to be significant difference in meaning in the right context between using arrêter de faire qqc or s'arrêter de faire qqc (italki link, previous comment from Cécile)

Interested to read others comments

https://www.larousse.fr/dictionnaires/francais-anglais/arrêter/5352.  https://www.wordreference.com/fren/arrêter 

https://progress.lawlessfrench.com/questions/view/arreter-vs-s-arreter-and-we-all-cross-fingers-vs-we-cross-all-our-fingers

https://www.italki.com/post/question-481364

Hi Jeramy,

Further to Maarten's post. Is it not the case that in the expression  "Je me suis arrêté de parler" the direct object is the reflexive pronoun "me"?

Jim

Hi,  I suppose what I was asking was if "j'ai arrêté de parler" is used in a transitive way as it is here then where is the object? If I said "j'ai arrêté un taxi" taxi is the object of the transitive verb.

I'm looking at a dictionary and it clearly states "s'arrêter = intransitve, arrêter = transitive"