Not quite.
Ofcom in their reply make their point clear: "The [Online Safety] Act explicitly grants Ofcom the legal authority to regulate online safety for individuals in the United Kingdom [...]"
They are stating that companies operating in the UK and providing services to UK individuals, are required to conform with UK regulations in relation to those services, under UK law.
As an American business, you can choose to ignore that, but that has consequences if any of your board of directors ever sets foot in the UK.
The US does this, and US lawyers understand this. If I open an online poker and sports bookmaking site in the UK (where such sites are completely legal), and take business from all over the United States thereby breaking federal law, I can expect to be met at the plane door the next time I take a shopping trip to NYC. Arguing that my servers and my business are located in the UK is not going to impress the federal judge I'd appear in front of in the morning. Stating the US laws against my activities have a snowball's chance in hell of being enforced in the UK is surely going to risk me being charged with contempt.
The Online Safety Act is ridiculous on many levels, but in the same way that Google does certain things in relation to Tiananmen Square searches in China, and every tech company engages in regulatory alignment for the entire Middle East, the UK has asked that US companies do certain things in the jurisdiction of the UK. I'd argue, less harmful and egregious things in some respects.
Should the UK do this? No, probably not. I think it will just make VPN software vendors richer, and UK citizens - particularly children - barely any safer.
Are Ofcom claiming jurisdiction in the US? No, they're claiming jurisdiction in the UK. Which, I hasten to add they are legally required to do by the Online Safety Act, by the government they are an agency of. If they didn't, the government would literally be breaking its own law.
TIL that 4chan's lawyer is about as grown up, mature and able to engage in critical thinking about the law as the people who post on his client's site.