Interesting. By joining an e-commerce or marketing company, doesn’t it also mean that software is seen as a cost center since it’s not directly the product being sold?

This is why I added the caveat. It's a culture question mostly but figuring it out is obvious when you think a bit about the kind of work you're doing. If your work is customer facing, there is a good chance you're selling a product. If its for internal use, there is a good chance you're selling something else and instead you're raw business value add, i.e. clear business benefit, given a budget with expected and clear returns. Left alone to make the magic happen.

Or to put it another way, if you're adding core value to the business proposition or enabling their core business you're probably not going to be seen as a cost center. If you're R&D or innovation focused, probably not a cost center.

For example, working on a Wordpress site for a newspaper, probably cost center unless they're extremely tech focused. NYT comes to mind, but they straddle the line between saas product and not. They're selling the subscription service which puts you in product camp but they also have engineering functions that work on enabling their writers produce content. The content is the thing being sold, not your software so its probably some mixed feels over there.

I should probably extend the original "ecommerce or marketing" to any more traditionally non tech business model that has built itself as a tech company. For example:

Working on a website for an architecture firm = cost center.

Working on cad plugins for an architecture firm to use internally = probably not.

And again, caveats, even for ecommerce you could be considered a cost center if the business is more like a traditional brick and mortar but they've "started selling online".