That's Hero's aeolipile, mentioned near the end of the article.
Most scholars tend to agree that Rome [1] was nowhere near an Industrial Revolution. One take on it is here: https://acoup.blog/2022/08/26/collections-why-no-roman-indus..., but the general tl;dr is that a) even if you backported a fully working Watt steam engine to Classical Antiquity and they could manufacture it, there's nothing that they could use it for [2], and b) the Roman economy isn't really in a shape that encourages the kind of industrial innovation feedback loop you see in the Industrial Revolution.
[1] Side note: at the time the aeolipile is developed, there is no independent Greece; Rome thoroughly conquered all the polities in the Balkans in the 2nd century BC. Classical Greece is largely 5th century BC. The aeolipile dates to 1st century AD, rather late in Roman history.
[2] The historical motivation for the steam engine was of course draining coal mines, and the Romans weren't really using coal in enough quantities to require it. The Industrial Revolution itself was initially jumpstarted with textile production, which Rome was even further behind in--the spinning wheel wasn't developed until after 1000!
You are correct as far as anyone alive today can know. I would just add that there was quite a bit of cultural aversion to non-agricultural enterprises among the senatorial class. Merchants and tradesmen were looked down upon. This was made worse as many skilled laborers in the city of Rome were actually slaves.
Most scholars tend to agree that Rome [1] was nowhere near an Industrial Revolution. One take on it is here: https://acoup.blog/2022/08/26/collections-why-no-roman-indus..., but the general tl;dr is that a) even if you backported a fully working Watt steam engine to Classical Antiquity and they could manufacture it, there's nothing that they could use it for [2], and b) the Roman economy isn't really in a shape that encourages the kind of industrial innovation feedback loop you see in the Industrial Revolution.
[1] Side note: at the time the aeolipile is developed, there is no independent Greece; Rome thoroughly conquered all the polities in the Balkans in the 2nd century BC. Classical Greece is largely 5th century BC. The aeolipile dates to 1st century AD, rather late in Roman history.
[2] The historical motivation for the steam engine was of course draining coal mines, and the Romans weren't really using coal in enough quantities to require it. The Industrial Revolution itself was initially jumpstarted with textile production, which Rome was even further behind in--the spinning wheel wasn't developed until after 1000!