I am not sure, too.
If I remember correctly they had no own pets - no dogs and no cats on the premises.
However, this place has a very busy common area/kitchen/reception. I could not imagine to bring a pet to this place.
The rest of the hostel is organized in the stories with balconies. Also here, I could not imagine to bring a pet is a good idea.
What kind of pet do you have?
Anyway, contacting Ronny, the owner, through the official email should bring quick clarification.
Get an answer from Sleepers Sleep Cheaper Hostel staff and past guests.