You're right, but "Mobile first" is the way they are describing themselves, it's the phrase used in the jobs link I posted. And I would personally interpret "mobile first" to imply native apps in just about any context, so I think it gets the point across.
I would personally interpret "mobile first" to imply native apps in just about any context
You're part of a growing minority who interprets it that way. Google search results for "mobile first" are still very web-focused today, but I'm concerned the native app community will usurp that phrase, confusing everybody.
And while I'm speaking for the web community, apologies for usurping the word "responsive" and confusing everybody.
should be
"They are building a web version, they're just doing native apps first"
Doing mobile first can totally be web.