I've boldfaced any non-Shotokan forms and attempted to note their origins. If I listed a question mark, I do not know or cannot recall their origins from memory. So, I guess we can see that TSD is drawing from many different styles of karate (and some Chinese martial arts). Feel free to add to this list if you would like. It looks like a good bit of the Goju Ryu syllabus is there.
I'm disinclined to believe Goju-ryu played much of a role if any in the development of Tang Soo Do. The lack of Sanchin training, complete absence of mawashi-uke in any of the accepted TSD forms, dearth of kakie exercises... The evidence, or lack thereof, connecting the two arts is pretty definitive to me. I'd also offer up the Chil Sung forms created by GM Hwang... Again, no Goju influence there to my eyes.
It looks like GM Hwang simply wanted to list all the known classical karate forms he knew of in his book. That in of itself is not evidence that he knew or practiced them.
Here's some of the translations I sounded through, not knowing Korean nor Japanese. The standard kata in Goju-ryu are well known: Sanchin, Gekisai Dai Ichi, Gekisai Dai Ni, Saifa, Seiunchin, Seipai, Shisochin, Sanseiru, Seisan, Kururunfa, Suparinpei, Tensho
Dam Toi = Tam Toi (a common beginner set with many variations across Chinese styles)
Rohaee = Rohai (Funakoshi Sensei is thought to have created the Shotokan kata Meikyo using elements from the Okinawan Rohai kata)
Woon Shu = Unsu
Tsan Tjin = Sanchin
Jun Jang = Tensho
Sei San = Seisan
Goo Reung Hoo Ah = Kururunfa?