Not quite. It bans new government-run broadband everywhere regardless of whether or not there would be private competition in the area. In areas that already have government-run broadband, it allows that to continue as long as that area does not have more than one private provider.
It says in 2(a):
> Except as provided in subsections 3(b)(1) and (c), a State or political subdivision thereof may not provide or offer for sale to the public, a telecommunications provider, or to a commercial provider of broadband internet access service, retail or wholesale broadband internet access service.
Subsection 3(b) starts thusly:
> Any State or political 9subdivision thereof providing or offering for sale, either to the public, a telecommunications provider, or to a provider of broadband internet access service, retail or wholesale broadband internet access service, before the date of the enactment of this section
and continues in 3(b)(1) (the first exception mentioned earlier):
> notwithstanding subsection (a), may continue to provide or offer for sale such service if the Commission finds there is no more than one other commercial provider of broadband internet access that provides competition for that service in a particular area
and on 3(c) contains the second exception:
> Notwithstanding subsection (a), this section does not apply to the Tennessee Valley Authority
The article you posted said something else, that the bill was to ban government-run broadband in an area that has private competition.
From your link: