The Supreme King Deck doesn't have a really articulated play style by itself given its small membership but can work effectively as an engine. Using "Supreme King Dragon Darkwurm", the player is capable of toolboxing into the "Supreme King Gates", the archetype's main sources of a Pendulum Scale. Since both "Supreme King Gate Zero" and "Supreme King Gate Infinity" have Scale values of 0 and 13 respectively, they can potentially allow for monsters of any Level to be Pendulum Summoned, although "Infinity" carries a restriction of controlling no monsters in order to Pendulum Summon. So far, there is only one Ritual monster in the archetype, Demise, Supreme King of Armageddon which specializes in the destruction of every card on the field, inflicting 200 points of damage for each card destroyed that way.
For starters, most of them are DARK monsters so they cannot conflict with the Pendulum Effect of "Darkwurm". Secondly their Pendulum Scales have values of 1 and 8, which mix well with the "Supreme King" cards since "Darkwurm" is a Level 4 and both "Gates" are Level 7. Thirdly these "Magicians" along either "Astrograph Sorcerer" or "Chronograph Sorcerer" are one of the ways to Special Summon "Supreme King Z-ARC", the archetype's boss monster. Additionally, the effect of "Darkwurm" to Special Summon itself from the Graveyard makes it a useful discard fodder for cards such as "Pendulum Call" as the player can instantly gather the means for a Pendulum Summon for no cost and their Pendulum Scales will go uninterrupted.
As a result of this mixture the "Supreme King" archetype is capable of more moves, involving greater flexibility in both Pendulum Summon and other Summon mechanics, being able to perform Fusion, Synchro and Xyz Summon.
Finally, for Xyz Summoning, the archetype can gain easier access to either Rank 4 or Rank 7 monsters, ranging from utilitarian ones such as "Dark Rebellion Xyz Dragon" or "Timestar Magician" to the likes of "Number 11: Big Eye" or "Odd-Eyes Absolute Dragon". "Darkwurm" is interesting due to its self-revival ability from the Graveyard which potentially mitigates some of the otherwise common and taxing cost of Pendulum-Xyz tactics. After dumping the "Z-ARC" Magicians by detaching them, they can then be banished for "Z-ARC".
For Pendulum Summoning, other additional and more mainstreamed cards such as "Odd-Eyes Pendulum Dragon" or "Archfiend Eccentrick" can be useful as well. The former can search either of the "Gates" and many of the aforementioned "Magicians", while "Eccentrick" is an effective removal card. In other words, the "Supreme King" archetype is fairly flexible since they can be mixed with multiple cards and provide a handful of utilitarian uses.
As per the Master Rule 4, the deck loses its Pendulum Summon power. However, the player would often stand without Pendulum Summon as per the Pendulum Effect of "Infinity" thanks to the archetype's penchant for swarming and controlling the field through its "boss".
After swarming the Field with weaker monsters, the player can bring out "Supreme King Dragon" Extra Deck Monsters and use them to press the opponent. After your opponent gets rid of them and you managed to get "Z-ARC" on the field, you can use "Supreme Rage" to devastate, or even finish the opponent.
Since they are a Pendulum archetype, they are vulnerable to cards such as "Anti-Spell Fragrance" which can shut them down in the spot.
Their small membership demands that the player mixes them with something else to make the most of it, and thus more than likely adopt that Deck's weaknesses as well.
"Infinity" can be more trouble than an aid due to its "no monster" clause to perform a Pendulum Summon.
The player should also prioritize which summoning mechanic to boost while mixing and be selective of the cards to use for that purpose, as using too many cards can lead to unfortunate draws.