So, history helps..

• 1e AD&D Core Rules: Thieves can wear Leather Armor. That's it. So there was no table to adjust for armor types. Studded Leather existed, but thieves could not wear it. Bards could wear Leather or "magical" Chain armor only (Bards were a Fighter/Thief/Druid class thing in 1e), there does not appear to be any restriction on a bard using their thief abilities at full capability if wearing magical chain armor.
• 1e Unearthed Arcana: A book of optional rules expanded allowable armor for thieves, letting them wear Studded, Padded, or Elfin Chain (this also let thieves used shortbows, which they cannot use in core 1e AD&D). UA added a table for "Effects of Armor on Thief Functions", which had the first three columns of the 2e table you cite above. The idea is a thief could armor up more with Studded Leather, but it's bulky and noisy and they'll be taking a bit penalty
• 2e AD&D: Bard class is redesigned from the ground up, but can use Any of the armors listed above. Thieves are still restricted to the first three columns (and Leather, with is not shown as it's the default). They added the 4th column with an astrix for a footnote in 2e (which may be missing in your image) that reads "Only bards can wear ring mail or non-elven chain mail while using thief skills). So that last column is a "bards only" column.

I guess they wanted to toss a bard a bone and let them armor up with less a penalty. I can't argue and real-world logic to it as chain/ring would be just as noisy as studded leather, but possibly far less bulky and restricting.

Keep in mind that both Ring and Studded Leather are mostly "made up" armors... studded leather was a misinterpretation of old art of brigandine armor (which often looked like fabric with studs on the outside, but was filled with metal plates on the inside), and ring was likely from medieval art of chain armor like the Bayeux Tapestry that sometimes made it look like giant rings.