Why would China and the EU have input on a US merger?

Because Intel, AMD, etc have offices in EU and China, for sales, distribution and also R&D. If you intend to operate in those markets you need to comply with local regulations.

The same reason as anything else. If the merger goes ahead with opposition from foreign markets, those markets can impose import tariffs or outright bans. Smaller markets may be ones these combined companies are willing to piss off, but not Europe. Their opposition is defacto a deal killer.

They literally don't any serious homegrown alternative though, they'd be effectively forfeiting the AI race

China doesn't care. They are banned from buying western AI HW or making their own AI HW at TSMC/Samsung. They are pouring hundreds of billions to the semiconductor ecosystem.

Huawei is trying to make establish domestic Ascend/MindSpore ecosystem, but they are limited by the SMIC process (~7nm). Amount of defects is allegedly rather high, but they are the only "official" game in town (other than smuggled NVIDIA cards or outsourced datacenters in Middle East).

Then the point about China trying to block a Nvidia merger doesn't really sense if they will be going their own path anyways. It would exist to try to harm Nvidia before their homegrown alternatives ramp up.

Nvidia is only one side of merger. The other is Intel. Intel does sell processors in China. Only AI is banned, not generic CPU (except HPC).

> Why

Well they obviously would..

Also EU has promised various significant subsidies to Intel. They obviously has fabs in Ireland and building one in Germany and perhaps even Poland..

If this is a rhetorical question, just make your point instead.

If not, look up e.g. Microsoft 's purchase of Activision, both US companies.

Do they want to sell pentiums in China or EU?

They wouldn't, but companies at this scale are global, regardless of where their nominal headquarters or stock listing is.