> Seems like any web browser by a for-profit company would immediately be in breach
A web browser cannot be in breach, because a web browser is not a legal entity capable of being a party to an agreement. The entity in breach would be the person using the browser, if they were using it in a way that was against the TOS.
BTW, that TOS is ambiguous. I see two ways it can be parsed. First,
> You may not (copy, display, distribute, download, license, modify, publish, re-post, reproduce, reuse, sell, transmit, use to create a derivative work, or (otherwise use the content of the Site for public or commercial purposes))
I.e., "otherwise use the content of the Site for public or commercial purposes" is one item in the list of prohibited things. Second,
> You may not (copy, display, distribute, download, license, modify, publish, re-post, reproduce, reuse, sell, transmit, use to create a derivative work, or otherwise use the content of the Site) (for public or commercial purposes)
I.e., "otherwise use the Site" is one of the list items, and "for public or commercial purposes" modifies the whole list?
If it is the latter it is saying you can do what you want if it is not for public or commercial purposes.
If it is the former, it is saying you may not do any of the explicitly listed things, and you can't do anything not listed if you are doing that thing for public or commercial purposes. You can only do things that are not explicitly listed and then only if they are private and non-commercial.
I'd guess they meant the latter, because under the former it is hard to see any way to use the site at all without violating the TOS. If that is the case, they should have written it as "You may not for public or commercial purposes <list of things>".
On the other hand, it would't actually be all that surprising for a big company to write a TOS that technically prohibits their users from actually using the site, so who knows?