Shouldn't this be "I'm walking" in English? "Sétálok" is a present continuos action.
It can be either one.
Mit csinálsz minden reggel? - What do you do every morning?
Sétálok. - I walk.
Hungarian lacks the infinitive case, and is the same for both English infinitive and present cases.
I am not sure what you mean by "infinitive case". Can you please elaborate or give a few examples?
Any chance you are referring to the continuous or progressive tenses?
Yes, Hungarian has only simple present and simple past, the progressive sense is not expressed grammatically.
"to walk" is the infinitive tense – "walking" is present tense. — I should probably use "tense" and not "case". For what I've learned, Hungarian doesn't make a distinction between "I walk" and "I am walking".
"To walk" - is the infinitive. The Hungarian equivalent is "sétálni". The "-ni" suffix makes it the infinitive.
I like to walk. - Szeretek sétálni.
"I walk" - is the simple present tense.
I walk. - Sétálok.
"I am walking" - is the present continuous or progressive tense.
I am walking. - Sétálok.
Yes, these last two are not grammatically separated in Hungarian. There are other ways to express the difference, when needed.
Okay, so there's an infinitive case.
And by "present continuous", I think it's called "present participle"