and in no way supports the breaking of the terms.
It's a bump of their topic.
No, I mean their post isn't telling others to say PM their new account or otherwise bypass the ban.
The ban is deserved regardless of whether they have a business to run, and they should not be given special treatment because of it.
I think they should and it does. The ban not only affects that user and its business (fine), but the customers of that business (not fine). Their post constitutes the minimum infraction of rules while trying to keep their customers undamaged and informed.
That user was promoting his website in places he shouldn't have. Slipping his link and his "business" here and there in posts that were completely unrelated to the topic.
It's a kind of promotion, like commenting on websites with a genuine-looking comment but with the purpose of posting a link to your own website and doing some self-promotion. That is what this user is doing, and he/she is playing dumb every time they get called out.
I agree with you on that part, Stealing customers from other threads is a very shady method of promotion.
IIRC, hilariousandco warned him/her some time back to stop posting only for the purpose of self-promotion and it doesn't seem like he/she got the point.