The World of Trophies, also known simply as This World (この世界) according to the Smash Bros. DOJO!! website and some trophy descriptions, is the setting in which The Subspace Emissary takes place. According to Master Hand's trophy description, he is the ruler of this realm.
Although it is never explicitly stated, it can be assumed that Super Smash Bros. Ultimate's Adventure Mode, World of Light, takes place at least partially in the World of Trophies, making it a pseudo-sequel to The Subspace Emissary. This is most evident in the opening cutscene, where the initial fight against Galeem seemingly takes place on the same cliffside that formerly showed the Isle of the Ancients on the horizon as shown during the final Subspace Emissary cutscene. It should be noted that the world is destroyed and rebuilt following this cutscene, which explains why the in-game map is completely different to that of the one featured in The Subspace Emissary.
Daemon Rising with a...SMASH![]
In the ReBoot Multiuniverse, this was actually named the Smash System, where all the Champions lived in different Sectors of the System, similar to those who live in Mainframe. Much like the World of Trophies, it too was ruled by the deity, who soon became a Guardian and merged Key Tool, Master Hand! This was the singular world highlighting the locations in Melee's Adventure Mode such as Peach's Castle and the Mushroom Kingdom, the Big Blue sector, Hyrule and its ruined Temple, the kingdom of Alita, etc.
During the Net War, Samus was the first Guardian being noted of Daemon's oncoming threat as she headed to the Smash System from Mainframe before it was sealed by Mouse's Firewall. She met up with Mario, Peach, and Luigi fending the Castle from an invasion by Bowser before her Gunship landed. Master Hand eventually appeared and heard the news, and he ordered his warriors to recruit everyone, otherwise he'll resume the tourney, much to Luigi's dismay. Samus and company gathered all the fighters at the rendezvous point; unfortunately, Master Hand sensed Daemon spreading out her infection in the sealed Systems via the infected Guardians' Seeds. He became distraught, but the Smashers never gave up.
Their allies encouraged them to keep fighting, thus the war was taken at Mainframe! By the time each of Daemon's cronies were defeated, she was a hair close to the Portal leading to the Smash System awaiting the "messenger" to infect it. Outraged, Mewtwo and Samus stopped her, and she challenged Bob to fight him in the Brinstar Depths beneath the Zebes Sector. While there, she never hesitated to fight back, despite losing to his Glitch powers, Kraid swiping the stage, and Pikachu temporarily assisting her. Eventually, her determination helped her win.
She and Mewtwo confronted Daemon again as she had no more challengers, so they took the last battle to Final Destination! Master Hand intervened, only to be churned into a Trophy provided by him which was originally made for Daemon; he touched her infection, and Samus threw in the Stand as a sacrifice. She and the Pokémon went all out, even several of Akari's Pokémon to stand up to the tyrant before they were blasted away!
Eventually, the Falcon Flyer came to their aid as it left the Super Computer, and Akari threw in a Trophy Stand toward Daemon reducing her to a trophy and disallowing the infection to spread despite her shattered hourglass. Samus fired onto the trophy, which accidentally allowed it to spread and cause the Falcon Flyer to crash land into Mainframe, while the Smash System was being cured by Hexadecimal carrying the cure via her masks as she was being defragmented.