So I can't say on THE tall chairs? Is there really a difference here?
You can't say "the high chairs" because there's no "the" in thr Hungarian sentence. When there's a "the" in English, there will almost always be one in Hungarian too.
I can't hear the s in magas either. I think it blends into the initial sz of székeken in a way that a native speaker might be able to tell the s is there but is tough for a learner.
In the audio, I don't hear the "sh" sound in "magas". Is there a reason for that?
Because in English "tall" and "high" do not mean the same thing. "Tall" is of greater than average height while "high" is a long way above the ground. A chair would be "high" if it was hanging on a hook from the ceiling. Further the term "high chair" has a special meaning as a chair with long legs and a tray for children.