It is the difference between indeterminate and determinate aspects. Most verbs just have perfective and imperfective aspects, but there is a few number of verbs that are further divided into determinate and indeterminate in the imperfect aspect. Determinate means action in progress while indeterminate means habitual or frequent action. So here biegam (biegać) means I run "regularly" or "everyday" and so on while biegnę (biec) means I am running "at the moment." I wish Duolingo's Polish grammar chapter was available especially for this section, but only the beginning sections seem to have the grammar notes.
I realise that it's the Polish we should really be concentrating on, but to this (BrE) native speaker and EFL teacher "I am running every Tuesday" certainly doesn't sound more natural, and might well be marked wrong in an English exam for foreigners.
I agree, however, that we we're unlikely to use the simple "run" very much either, but at least it's grammatical.
The most natural, of course, is "I go running every Tuesday". We tend to use verbs like "run, swim, cycle" etc with "go" rather than on their own (one of Duo's little foibles). But I accept that could be a bit confusing here.
If I were to say I am running every Tuesday, I think it would be that I have made a decision as of late to do the running every Tuesday, If I say I run every Tuesday, that decision to run is no longer a consideration and the focus is on the fact that I run regularly. In the former, perhaps the person was explaining a new lifestyle, or a new schedule, perhaps towards another goal.
Perhaps the words are more strict in Polish. In English "Running" is considered to be an activity as well as a verb. So someone would be describing what they are doing, every tuesday, when they say "I am running..." .
When one says "I run..." it almost sounds past tense, and doesnt convey the same on-going status . Thats how it sounds to me.
English has many way of saying quite literally the same thing, as many words and statements are actually pretty vague.
I just posted something similar on the "Rzadko biegamy w parku" page. I wrote 'I go running every Tuesday', which came up as wrong. The answer it gave me was 'I run on every Tuesday'. No-one would ever say that. The gerund should be allowed here with go. But I know it's not the exact translation, but its the most natural translation for me. Even 'I run every Tuesday' is pretty uncommon if you ask me.