This is not synthetic life. It's synthetic DNA! DNA is not life. This is shown that when a cell dies it has exactly the same DNA it had before it died. The DNA is the software for the cells hardware. Just as a computer can run different software so a cell can "run" different DNA. Now your computer will just sit there without software to run it and so will a cell until it dies.
Why this is such headlines I have no idea. When I worked at the USDA in Albany California we were injecting sequenced DNA into plants cells all the time. This was twenty years ago! This is the first time that a complete genome has been sequenced but it's not life, it's DNA.
If you have a dead cell and inject sequenced DNA into it you will have a dead cell. You have to start with a live cell to get a live cell after the DNA is removed and the new DNA is injected.
The reason, I believe, that this is such headlines is there is no good definition as to what is life. This is a huge problem with the search for extraterrestrial life. How will we know life when we see it if we have no definition of what life is?