"Gouki" have wrestling themes in design and name, shown in the fact that they wear tights and golden championship belts. While each of the Main Deck monsters are based on an animal, the Extra Deck monsters are based on Ogres which they draw heavy elements from. Their championship belts have the face of their themed animal, and their helmets fit the theme of their animal as well. They are also suited up in padded armor and wield weapons. They possess a predominantly single colored theme. So far, the Main Deck monsters each have a primary/secondary color while the Link Monsters are a neutral color. These monsters resemble, in terms of style, the "Elemental HEROes".
"Gouki" (剛鬼) can be translated as "strong ogre", but it's likely a pun on the word 剛毅 gōki ("hardiness, manliness"). The Main Deck "Gouki" monsters are named after wrestling moves, such as Suplex, and then their appearance is based off an animal whose name is in the wrestling move name, being based off of their respective animal, or creates a pun based off that animal's name, that phonetically sounds in their romaji, such as "Gouki Suprex" being a pun on T-Rex (SupREX).
The "Gouki" monsters seem to focus on a straightforward aggressive strategy, using effects to increase their ATKs or decrease the opponent's. The Main Deck monsters have 0 DEF, being immune to the effect of "Gouki The Great Ogre", who, in turn, has no DEF; that makes it so that they generally have an advantage over the ATK of opponent's monsters', since theirs' will likely end up reduced while yours' w'on't.
Additionally, the Main Deck "Gouki" monsters released up to Cybernetic Horizon all share this effect "If this card is sent from the field to the Graveyard: You can add 1 "Gouki" card from your Deck to your hand, except [itself]". This keeps you from losing unneeded card advantage upon using them as Synchro/Link Materials, or with cards like "Transmodify", "Downbeat", and "Spiritual Earth Art - Kurogane".