If a company has built software to run their service in different places (Windows, Mac, Linux, Set-top boxes, Game consoles, etc) then these would be called what?
The term needs to show that it was software built for that platform specifically.
Native Clients? Native Platforms? Something else?
Precise terms varies, but in general it's simply client application. If you want to underline that is runs on a specific platform, then you can say native client.
If you want to underline the fact that it supports many platforms or that it is practically "platform-independent", then you can say it is a multi-platform application. But then you're talking about the product as a whole, not the actual application (unless it is e.g. a Java application or a web-based application).
If you're simply looking for an antonym to General Purpose Software, then you're looking for the term Special Purpose Software.
I want to clear out some misunderstanding you seem to have, since your question implies that you do not fully understand all the terms you're using:
software they built for purpose, not just open source software
The antonym to (free) open source software is proprietary software.
Proprietary software is software which has undisclosed source code. However, proprietary software may also be general purpose software (such as commercial off-the-shelf, COTS, software), and open source software may purely be special purpose software too - licensing and purpose are not mutually exclusive.
And lastly: the term you proposed, "native platforms", is kind of an oxymoron; native software is software specifically compiled to a specific platform. The term "native platforms" doesn't have an apparent meaning.