Let me put it this way; they're remakes of Yellow, Main Series games. Why wouldn't these be main series? Besides the fact they said so. Another way to look at it is one set is the main storyline games, which are the usual 8 gym leaders, etc. While the other games still fit into the story, but don't follow the same core gameplay design. Which is likely what they meant by "core".
A lot of franchise have core games, but have other games that still are canon, but not a core game. Sonic, for instance. There's tons of non-platformers that are still part of the series, but don't fit the core gameplay of being a platformer. Whether you want to call them spin-offs or not is irrelevant. There's non-canon and canon spin-offs. Canon spin-offs are part of the main series, basically.
Hope this explains the reasoning behind it better. It does make sense, it's just a really weird way to say it.