Mr Baszucki founded the platform with Eric Cassel in 2004 and released it to the public in 2006 – a year before the first Apple iPhone appeared, heralding the start of the smartphone era.
Mr Baszucki describes his younger self as "less of a gamer, and more of an engineer", and the pair's first company was an education software provider called Knowledge Revolution. But they soon noticed that kids weren't only using the product to do their homework.
"They wanted to play and build stuff. They were making houses or ships or scenery, and they wanted to jump in, and all of that learning was the germination of Roblox," he says.
The name Roblox was a mash-up of the words "robot" and blocks" – and it stuck. The platform grew quickly in popularity – and there were also early warning signs of its future issues.
Mr Cassel noticed some players "starting to act out" and not always behaving in a "civilised" way a couple of months after it launched, recalls Mr Baszucki.
He says the roots of building a "trust and safety system" therefore began "very, very early" and that in those earlier days there were four people acting as safety moderators.
"It kind of is what launched this safety civility foundation," he adds.
But despite attracting decent numbers, it was a year later, when the firm launched its digital currency Robux, that it really started to make money.
Players buy Robux and use it to purchase accessories and unlock content. Content creators now get 70% of the fee, and the store operates on dynamic pricing, meaning popular items cost more.
Mr Baszucki says there was some initial resistance among the leadership team about Roblox becoming more than a hobby for its players, with the introduction of a digital economy.
Robux stayed, and the firm is now worth $41bn (£31bn).
Its share price has fluctuated since it went public in 2021, but overall Roblox shares are worth about one third more than they were six months ago, at the time of writing. Like many big tech firms its value peaked during Covid, when lockdowns meant millions of people were indoors.
Mr Baszucki compares his experience of building Roblox with how Walt Disney may have felt about his creations.
He describes his job as "a little like having the opportunity he had a long time ago when he was designing the Magic Kingdom", and is focused on Roblox's ongoing evolution into a Metaverse-style experience where people go about their daily lives in a virtual world, in avatar form.
They have also been public in their ambitions to eventually attract 10% of the world's gamers.
Asked to describe Roblox in three words, he replies: "The future of communication."
We finish our time together playing a couple of his favourite games: Natural Disaster Survival and Dress to Impress.
We use his account and he's constantly recognised by other players — but we still get smashed to pieces by a blizzard outside the Natural Disasters mansion.
Additional reporting by Ammie Sekhon
