If someone were to ask if I and a friend were running in the upcoming race/ road run, I would say "I'm running, and so is she [running]."
"I am running" is perfectly fine, and not uncommon, in context. Further, in the right context, I suggest that MOST people would say it, contrary to your assertion.
My understanding is that laufen means "to ambulate"; to move somewhere by the power of your own legs. That can be either running or walking. You need context to get a sense of which. I think rennen is closer to "to race" which is why you can refer to cars that way as well as people. Spazieren is nice and easy, that is "to stroll". Someone please correct me if I am wrong about any of these!
If German doesn't have a present continuous "I am running" why is an English translation of " I run and she runs too" incorrect? Surely a correct translation could be either (run or running) and in English the translation would be determined by the context. There is no context here.