Project starshot does have a history, beyond this press release. And they have thought through the issues. There's a great youtube video here that goes into the details:

https://www.youtube.com/watch?v=bbi1hHPpTjY

They talk about using a 1km^2 earth based laser array to accelerate the craft. They also discuss using a 1W laser on the craft, and using that to transmit data back to earth (with a similar 1km^2 array to receive the signals).

They really seem to have thought through all the issues and come up with difficult, but plausible solutions.