The kanji "中" means that the stream is currently being done? Usually it put something in gerund but I don't see what it's doing there. There is no gerund in my translation.
I'm not sure what you mean by 'put something in the gerund'. I don't see why 中 would create translations with gerunds particularly often.
In any case, it can be used to mean 'in the middle' or 'inside of' (physically), (海中、車中、手中、地中) or it can be used to mean 'in the middle of (doing)' or 'during' temporally (仕事中、工事中). 「配信中」 is in this category.
These meanings can occur with all the readings ちゅう、じゅう、and なか, but ちゅう or なか are most common here.
Just for completeness there's a third common usage which is 'throughout the duration of' (一晩中、年中). This meaning can appear with all three readings also, but じゅう is most common here.
There's also a set of compounds that use figurative or idiomatic sense to describe mental or emotional states (集中). I don't believe these uses are ever as a simple suffix, but will always be a set dictionary word.
Because of the multiple readings across various meanings, you'll often have to consult a dictionary to learn the correct reading of a given compound. Meaning can often be deduced ... 中 appended to a physical thing likely refers to the inside of that thing, while 中 appended to an activity likely refers to the period in which that activity takes place.