"synthetic" in this case means the DNA is extracted from one cell, sliced and diced to get a desired genome, and then injected into an existing cell to hijack its offspring to use the new "hacked" DNA. Is that accurate?
In my mind "synthetic" means starting from basic chemical compounds and building from the ground up to create a desired molecule.
This seems more like if you took a big box of hard drive parts (cannibalized from existing computers), cobbled together a working hard drive, and then stuck it into a computer and then claimed you've "synthesized" a computer.
The actual design itself was heavily based on the genome of a natural organism, M. mycoides. They sequenced its genome and built an experimental dataset of which genes were essential and which weren't, then designed and printed a genome using the native sequences of just the essential genes.
Work on synthetic cells is now moving in a few directions, including designing the genome from scratch and building cellular or cell-like chassis to 'run' the genome.  Even in designing a genome from scratch, however, we would still be using proteins sourced from nature, because our ability to design proteins is still very limited. One way to think of this is that the biological world provides a massive pre-designed parts catalogue, and then we can compose those parts in a synthetic genome.
I'm a graduate student working on building a cell , happy to answer any other questions you might have.
 Like Twist, https://twistbioscience.com/
Just to be pedantic, but insightful (hopefully) those 'assembly' stages were in other host organisms (e coli, first, via Gibson assembly, then, yeast using TAR cloning) -- I worked in that lab.
Venter's first "synthetic" bacterial cells had their nuclear genomes ejected and then replaced with genomes copied from pre-existing cells. It would be extraordinarily hard to create a cell from scratch without all of the existing biology ("to make an apple pie, first construct the universe".)
These genomes contain an abundance of genes, some of which are suspected to be inessential in maintenance of life and proliferation under normal conditions (ie. they signal pathways or encode structural or metabolic components that aren't absolutely critical).
Venter's work here is to identify a minimum viable set of genes required to run chosen from an existing, easy to grow bacteria. Such an organism (or set of organisms) would be much easier to study as there is less noise. The biochemistry gets much simpler.
To be clear, this isn't the minimum set of genes required to live. It's the minimum set of genes required to run the bacteria it is modeled after. Different experimental parameters may necessitate deriving similar minimal organisms from different species. Or introducing additional genes (eg. resistance genes).
Eventually, once these "synthetic" bacteria have been proven, labs will want to order them and conduct their experiments under these much "cleaner" experimental models.
An article  was posted to HN a while back that gives me pause at that statement. Sometimes, perceived noise is signal and washing it out gets misleading results. Yes I'm sure this will make some experiments easier... but if it's for medical science... I have concerns.
Once they had an assembled chromosome (I believe it was a single ring), the scooped out the dna form a different strain of bacteria, placed their DNA hoop into the empty one, and it reproduced.
So, it is still a far way from starting with beakers of the elements, but certainly a bigger accomplishment than slicing some genes out of an existing bacteria.
They tried paring down a genome to its essential elements and failed. They then combined their designed genome with bits and pieces cut out from the larger, original genome, mixing and matching parts until they found the smallest subset of "parts" needed to run a fully self-replicating cell. The closest CS equivalent is that this was a kind of genetic algorithm with a focus on making a small codebase that minimally accomplishes replication, starting from a set of known-to-work pieces of code.
Open questions remaining:
- They found 149 genes of unclear function that were required to enable replication, what do those genes do?
- If you make a cell this way, how good is it at surviving? In culture, many model systems (yeast, e. coli) outcompete everything in the media by being faster at reproducing themselves (among other strategies). If these cells barely reproduce, other contaminating cells will go faster, making these minimal cells not very good for actual synthetic biology tasks without further modification (maybe they make a toxin while being immune themselves).
While I'd say that would be a far more accurate name in this story, I doubt their marketing department would like that...
As a field, it does seem a lot like scrounging through a parts bin for things that fit what you're looking for.
But that's fine; we know so little about biological systems, and they are so enormously complex. Plus, the documentation is non-existent and nobody can get in touch with the project's maintainer.
You could do it entirely by accident, but it's very unlikely.
EDIT: I should clarify, this is for human-infectious viruses. Human viruses are hard to grow because they require human cells or higher-organism cells to reproduce. That sort of tissue culture is very hard to do. Doing the mutation screening etc. is also quite hard to do in those viruses. CRISPR helps a bit, but there's a whole lot else that's still quite technically and biologically hard.
The other problem is keeping it secret. The chance of making a global catastrophe virus without any population testing and iteration is currently extremely, extremely small. It has now become quite easy to sequence DNA, so if a few people got seriously sick from a weird virus (perhaps a failed test version), the CDC or whoever would be able to sequence the viral genome whereupon it would probably be quite obvious that someone was making a designer virus.
The final point to make is that the kind of rationality, dedication, dilligence and technical skill required to engineer viruses doesn’t overlap much with the desire to destroy humanity.
I recommend this article:
"As D.I.Y. Gene Editing Gains Popularity, ‘Someone Is Going to Get Hurt’", By Emily Baumgaertner (May 14, 2018)
You would need to deliver some sort of an evolutionary pressure to the cells to shed any unnecessary genetic material.