He was running
It makes no sense to think of "running" as a gerund or noun in this example. Running as a noun would make sense in a sentence such as "Running is fun" or "He enjoys running". It would not make sense in "He was running" - which would mean "He was [the activity known as running]". A person can't be an activity.
Now, if you thought of "running" as an adjective, it would make more sense (but would still not be the most natural parsing of the sentence), and there are many participles that double up as adjectives - for instance, "amazing". It makes more sense to interpret "amazing" as an adjective in "He was amazing" than as a verb, whereas if the sentence was "He was amazing the children" then it's clearly a verb.
Similarly, if the sentence is "He was running a marathon" or "He was running ten metres" or "He was running the length of the road" then it is clearly a verb.