The New York Times also hosts Professor Turley's Written Statement, it's extensive (53 pages long) and I'll refer to that to answer your question.
Who are these missing witnesses? Are they the same members of the administration that Trump forbade to testify to the House?
It appears so and the reason (at least as Professor Turley argues in his written testimony) to allow (for a lack of a better word) the administration to prevent witnesses from testifying is privilege.
In his written testimony, the following paragraph on having testimony from key witnesses seems relevant:
In the current case, the record is facially insufficient. The problem is not simply
that the record does not contain direct evidence of the President stating a quid pro quo, as
Chairman Schiff has suggested. The problem is that the House has not bothered to
subpoena the key witnesses who would have such direct knowledge. This alone sets a
dangerous precedent. A House in the future could avoid countervailing evidence by
simply relying on tailored records with testimony from people who offer damning
presumptions or speculation. It is not enough to simply shrug and say this is “close
enough for jazz” in an impeachment. The expectation, as shown by dozens of failed
English impeachments, was that the lower house must offer a complete and compelling
record. That is not to say that the final record must have a confession or incriminating
statement from the accused. Rather, it was meant to be a complete record of the key
witnesses that establishes the full range of material evidence. Only then could the body
reach a conclusion on the true weight of the evidence—a conclusion that carries
sufficient legitimacy with the public to justify the remedy of removal.
Later on his written testimony, he talks about getting these witnesses to testify if the executive branch claims privilege (emphasis mine):
There is a third branch that is designated to resolve conflicts between the two
political branches.In recognition of this responsibility, the Judiciary ruled on the Nixon
disputes.In so doing, the Supreme Court found executive privilege claims are legitimate
grounds to raise in disputes with Congress but ruled such claims can be set aside in the
balancing of interests with Congress.What a president cannot do is ignore a final judicial
order on such witnesses or evidence.
Finally, some names are mentioned in his written testimony (emphasis mine):
Instead, it will proceed on a record composed of a relatively small number of witnesses
with largely second-hand knowledge of the position.The only three direct conversations
with President Trump do not contain a statement of a quid pro quo and two expressly
deny such a pre-condition.The House has offered compelling arguments why those two
calls can be discounted by the fact that President Trump had knowledge of the underlying
whistleblower complaint.However, this does not change the fact that it is moving
forward based on conjecture, assuming what the evidence would show if there existed the
time or inclination to establish it.The military aid was released after a delay that the
witnesses described as “not uncommon”for this or prior Administrations.This is not a
case of the unknowable.It is a case of the peripheral.The House testimony is replete with
references to witnesses like John Bolton, Rudy Giuliani, and Mike Mulvaney who clearly
hold material information.To impeach a president on such a record would be to expose
every future president to the same type of inchoate impeachment.