You don't say where you accessed this record, but I suspect it was via Ancestry's database. I went to the US National Archives' Access to Archival Databases (AAD to see if I could learn more.
For the field BRANCH: ALPHA DESIGNATION the help says, in part:
NARA prepared the code translations for this field based both on the
agency documentation and a review of the values appearing in the
records.
If you look at his GRADE: ALPHA DESIGNATION, it reads "Private". How can he be a private and a warrant officer at the same time?
This confuses me for a couple of reasons. I suspect I'm falling victim to 'presentism', trying to apply modern-day rules about pay grades and military rank to a period where they don't apply. We can glean some basic information and guidance from references like the Wikipedia article Uniformed services pay grades of the United States, but to answer the question fullly, we have to use the references cited in that article (specifically, reference 3, 37 U.S. Code § 101.Definitions) and then go back into the legal codes to discover what laws were in effect in December 1942.
We also have a problem in that we're looking at one record out of context, and not seeing this record as part of the surviving dataset, nor do we have access to the agency documentation NARA's team had when they were adapting these records for AAD.
However, there is one clue in the Wikipedia article Warrant officer (United States).
The article says:
In November 1942, the War Department defined the rank order as having
warrant officers above all enlisted grades and below all commissioned
grades.
But it also says:
On 21 August 1941, under Pub.L. 77–230, Congress authorized two
grades: warrant officer (junior grade) and chief warrant officer. In
1942, temporary appointments in about 40 occupational areas were made.
We have to remember that this is an enlistment record and the grade he enlisted at was one of the private grade. What I don't know without having the agency documentation, or being familiar with the whole dataset, is whether this code was used to flag the records of new service members whom the recruiter thought might be candidates for a temporary warrant officer rank. I am not experienced in this era of military records, so this is only a guess. see update below
The 1973 fire
You don't say when your grandfather separated from the military. That piece of information is critical to knowing what kind of access you can have to the records. Access is determined by a rolling window, as explained on this page: National Personnel Records Center's - Federal Records Center Program
Records are accessioned into the National Archives, and become
archival, 62 years after the service member's separation from the
military. This is a rolling date; hence, the current year, 2020, minus
62 years is 1958. Records with a discharge date of 1958 or prior are
archival and are open to the public. Records with a discharge date of
1959 or after are non-archival and are maintained under the Federal
Records Center program. Non-archival records are subject to access
restrictions.
If your grandfather served during WW2 and didn't stay in the military, he's likely to have been discharged prior to 1958. The next question is, did his file survive the fire?
NARA's page The 1973 Fire, National Personnel Records Center gives this estimate for the burned records for the Army.
Army Personnel discharged November 1, 1912 to January 1, 1960 80%
You won't know if your grandfather's file is one of the burned files until you ask. However, in addition to putting together files from other record sets, referred to as Auxiliary Records, NARA is still working on recovering some information from the burned files that were previously believed to be lost. See the following videos for more information:
Links to presentation slides, videos and handouts are available via NARA's Know Your Records program pages about the Virtual Genealogy Fair.
As I write this question, the research rooms at the NPRC are closed because of the coronavirus pandemic:
National Archives Closures for St. Louis Due to the coronavirus public
health emergency, National Archives research rooms and museums are
closed to the public until further notice and the National Personnel
Records Center is servicing only urgent requests related to homeless
veterans, medical emergencies, and funerals which may be faxed to
314-801-0764. We thank you for your patience and look forward to
resuming normal operations when the public health emergency has ended.
While you're waiting, you could learn more about his service by searching in historical newspapers, looking at home records, interviewing family members, and so on. Before you pay for a newspaper subscription, do a little legwork and collect some information about where your grandfather lived around the time of his enlistment, where other family members lived, and what newspapers were published in the areas where your family members lived.
The US Newspaper Directory at the Library of Congress lists what newspapers are in libraries, but it's useful as a crib to see what newspapers might be online. Check your local public libraries to see if they are extending access to historical newspaper databases that you'd ordinarily have to use in the library, and find out how to get an e-card if you don't have a card already. Browsing some full issues of a newspaper can give you a feel for how wide a particular newspaper reached for its audience. I have found many articles recently by re-doing searches statewide that I had originally done in papers "close to home", so start with a wide search and then narrow it down.
If you are lucky enough to find one of those social news snippets about what base your grandfather had been sent to for training, or a notice that mentioned his unit, you can look for unit histories and get an overview of what his unit did while you're waiting for the NPRC to re-open.
update
The technical documentation for this database is available via the US National Archives' catalog, and the data itself is available for download:
National Archives Identifier: 604357


As you can see in this code list, there are two different entries for the code BI. One is code 00 and the other is the two "high X punches" in that field on the card. I haven't looked at the downloaded raw data yet, but I wonder if these two values were collapsed when the database was created, and the wrong label was applied. Since the database was created from microfilmed images of the cards and not the punch cards themselves, errors are possible. It could be that your grandfather and other enlistees simply hadn't been assigned to a specialty yet.
To understand more about the nature of the database, and how NARA prepared it for publicaton online, see the online article The World War II Army Enlistment Records File and Access to Archival Databases by Theodore J. Hull, in Prologue Magazine Spring 2006, Vol. 38, No. 1 | Genealogy Notes.
Further reading: