Correct she does not explicitly say "my 1st Amendment rights were stripped away." Might've just been some unintentional/incorrect word choice by funhusker there.
But, she is trying to suggest her 1A rights were infringed for having her account restricted after what she said. I don't agree with her account restriction at all, however people need to stop conflating 1A rights to meaning they can say whatever they want on whatever platform they want. I think that's kind of what funhusker was getting at by I don't want to speak for them.
LinkedIn is a private company that can manage its community, for the most part, as it wishes. Now I don't support or really understand why they restricted her account just based off that one screenshot, but lobbying Freedom of Speech into there was just lazy and inapplicable.