It's obviously incorrect. It's not even really a logic error, it's a category error.
At face value the statement "if not all living things share a common ancestor, that makes them appear more like they were intentionally created" (although that line of reasoning, i.e. the watchmaker argument, has been debunked time and time again) seems reasonable.
However the statement seems far more grandiose than it actually is.
If two very "primitive" organisms (i.e. operating at a much lower complexity with much smaller and fewer moving parts than even, say, an earthworm) don't share their sets of DNA that may be unexpected (because whatever step there was from "not having DNA" to "having DNA" had to happen twice, separately, successfully).
If we found out that, say, all higher lifeforms shared no common DNA with other lifeforms outside their group and those groups closely aligned to the Christian "kinds" (which don't really map to biologically distinct groups in meaningful or consistent ways) THAT would be astounding.
But even that extreme case wouldn't make the "creation hypothesis" (if you even want to call it that) more plausible because it presumes the existence of an unexplained organism that is far more complex than anything it supposedly created. It doesn't explain anything -- it just shuts up questions about the "origin" by giving an answer that is impossible to analyse further.
There may have been a creator. But it's impossible to make a consistent logical argument for it. And it's entirely impossible to make an argument that that creator would in any way resemble something modern mainstream religions are worshipping.