No, the symbiotic relationship means that the bacteria live in/on the plant, much like we have a gut biome of organisms that are discrete from us, but have symbiosis with us.

The article is about a bacterium becoming engulfed within an algal cell and slowly becoming an organelle of that cell.

This process begins as a type of symbiosis, but at the end of it you would no longer call it symbiotic, as it ends as a single organism.

The breathless yammering about "the last time this happened we got plants" seems a little much though. The last time this happened that we know of was 1.5 billion years ago and we got plants. The fact we've caught it in the act right now sounds like this might just be a much more common phenomenon than we thought.

The article says

In the 4-billion-odd-year history of life on Earth, primary endosymbiosis is thought to have only happened twice that we know of, and each time was a massive breakthrough for evolution.

It's possible the only reason we're aware of these events is because they were massive breakthroughs. After watching it happen, we may have more information about how to spot other times it has happened.