"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' won'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".
When Gouki were first released, they were rather ignored in the competitive scene. The general consensus of top players was the Gouki Link Monsters were not strong enough or disruptive enough to compete with the top decks of late 2017 and early 2018, such as SPYRAL, Trickstars, and Pendulum Magicians, and there were not enough generic Link Monsters to make a non-Gouki Extra Deck.
However, in Flames of Destruction the Knightmare monsters were released, giving this deck a set of generic Link Monsters to utilise that could Extra Link and/or hand loop their opponent, providing a powerful end-goal for this deck to aim for going first. This strategy uses the card advantage generated by "Gouki"s in conjunction with "Isolde, Two Tales of the Noble Knights", "Knightmare Goblin", and most notably, "Firewall Dragon", to kick-start their plays. Once "Firewall" was Summoned, the player could repeatedly replenish their hand with "Gouki" monsters after the ones on the field were used as Link Material, and then immediately Special Summon those searched monsters, thus providing an extremely consistent stream of Link fodder for the "Knightmares" while losing little to no hand advantage in the process. Their usual end boards would consist of a combination of "Firewall Dragon", various co-linked "Knightmare" monsters protecting other co-linked monsters from various effects, "Tri-Gate Wizard", and "Topologic Gumblar Dragon", the last of which could use the hand advantage generated to force the opponent to discard up to 4 cards before they had a chance to make a play.
This deck proved to be the strongest Link Summon-based deck thus far seen in competitive play, with many other decks playing as many as 10 or more handtraps (the deck that won the 2018 World Championship played 16 in the 42-card Main Deck) just to try and stop this deck. Eventually, Knightmare Goblin and M-X-Saber Invoker were both banned to try and slow this deck's combos, and Called by the Grave was Semi-Limited to try and make handtraps more effective against it. It has continued to see competitive success but faded out of the scene after the deck's lynchpin, Firewall Dragon became Forbidden in January 2019.
However, note that because Link Monsters are immune to these strategies due to not having any DEF at all, these countermeasures do not work once the "Gouki" player has already established their board. This especially holds true for the Gouki Knightmare variant, which will often never end on a board with Main Deck Gouki monsters, and will often have negation and layers of protection from various card effects.
Disrupting "Gouki" plays before excessive co-links are established is vital for combating the Deck. "Ghost Ogre & Snow Rabbit" can destroy various combo enablers, and "Ghost Belle & Haunted Mansion" can desist "Gouki Re-match"'s effect. "Ghost Reaper & Winter Cherries" can also seal key Extra Deck monsters vital to this Deck's success. Competitive "Gouki" Decks rely much more on generic Extra Deck monsters such as "Topologic Gumblar Dragon" and "Firewall Dragon" (before its ban in the TCG) to fuel their plays. Thus, siding in "Ghost Reaper" against them incurs much less opportunity cost compared to doing so against most other Decks. All of these hand traps can be activated on the first turn of the Duel, making them reliable countermeasures if drawn into.