I regularly go out with a canicross group - that's people running with their dogs attached to them by way of harnesses and bungee lines.
While I was doing C25K I generally didn't count any 5k beginner runs the dog(s) and I went on as part of the training plan because there were often points on those where we had to stand around waiting for the very slowest person. That is I'd do say:
Wx R1, day off, Wx R2, day off, beginner run, day off, Wx R3.
This week, for the first time, I went on an intermediate (7k) run. I was the least experienced person there. Looking at Map my Fitness it looks like we did something like 5-6 min/k for 5 minutes then 4-ish minutes of jogging/walking, twice near the beginning of the route and then (partly due to my inexperience and partly due to the icy conditions) slowed down into a slower run a bit, walk a bit routine. We only stopped very briefly once.
Could I have counted that as an interval training day?
I'm using Active's 5k-10k app, and had to repeat week 1 after a fall, but I don't mind having gaps in the log on the app.