You are conflating two different matters. Of course someone with a Tier 4 visa can work outside the UK. Their Tier 4 work conditions do indeed only restrict or prohibit certain activities undertaken while the student is in the UK.
But the running, operating and managing of an overseas business would be undertaken while they are studying in UK, hence it would be prohibited.
The work conditions are in part about ensuring that someone's main purpose in the UK is their sponsored study. Running businesses and (as per your other topic) buying and renting out houses, or especially doing both, does not seem to be in that spirit. I would advise asking yourself, is this activity something I am perfectly confident is allowed, and I would be happy to tell the entry clearance officer that I plan to do it while I am studying in the UK? If not, don't do it.
uk-tier-4-student-visas/tier-4-student- ... l#p1857929
I do not give immigration advice. I refer you to Immigration Rules, guidance, other online content and to your sponsor.