It’s been a while since I did chemistry, so I’ll gladly be corrected, but I think I can get the ball rolling. The rows and columns of the period table are actually the really important part that unlocked modern chemistry once scientists figured out the structure of atoms. Initially, they were just grouped together like cards in solitaire (look up Mendeleev). In his version, it was a bit like what described. But, when we discovered how electron valence shells worked, we now had a way to connect the groups together. Because going across, each element has one more proton, which then tries to attract one more electron, which leads to many of chemical properties we know. And as you go down rows, you are filling out the valence shells this means that on the left side we always have a new shell with one electron (ripe for activity), and on the right we have a full valence shell (noble gases which don’t react much).
The beauty of it is that they figured all this out before they knew all the elements, so they literally had holes where they thought something would exist.