"Beszélgetek" specifically means "I have / I am having a conversation (with somebody)". So, it is a conversation, not a one-directional talk. Even if you are a teacher and you are telling something to a student of yours, that is not a conversation. For that I would say "beszélek" - without the frequentative "-get". The suffix "-gat/-get" makes it a repeated action, that is, when you say something, I say something, you say something, I say something, etc.
"Beszélek" means "I speak" or "I talk".
"Beszélek magyarul" - "I speak Hungarian".
A conversation is exchanging ideas, discussing some topic. If I "beszélgetek", that is usually not an unpleasant experience. If I want to take two weeks off, then I go and "beszélek" with my boss. Not "beszélgetek". But I frequently "beszélgetek" with my friends, family, etc.
I don't think "I talk" is the correct translation here. It needs context. I talk with somebody. Or "I have a conversation" is more accurate. Like what they do in a talkshow.