Various definitions abound. Here’s my stance. A website is interactive when there is some sort of two-way interaction that puts the consumer in the driver’s seat.
That said, it is possible for a website to be engaging, but not interactive. Yes, I mean who doesn’t like clicking? For example, the click-happy kook in you likely gets some measure of satisfaction in being engaged enough to click a Like button, click.
Does a Like button on a website make it interactive? I argue the Like button makes for a potentially engaging website, but not an interactive one.