Você precisa de INSERT INTO ... SELECT
, não SELECT ... INTO
Sintaxe oficial : INSERT INTO target [(field1[, field2[, …]])] [IN externaldatabase] SELECT [source.]field1[, field2[, …] FROM tableexpression
Tente:
INSERT INTO AllStaff1 (AllStaff.NAMEID, AllStaff.USERNAME, AllStaff.DEPARTMEN,
AllStaff.Lastname, AllStaff.Firstname, AllStaff.RFCARDNUMB, AllStaff.[PERSONAL R],
AllStaff.VENDOR)
select AllStaff.NAMEID, AllStaff.USERNAME, AllStaff.DEPARTMEN, AllStaff.Lastname,
AllStaff.Firstname, AllStaff.RFCARDNUMB, AllStaff.[PERSONAL R], AllStaff.VENDOR
FROM AllStaff
WHERE (((AllStaff.NAMEID) Is Not Null));
Isso não excluirá a tabela e deverá manter sua chave primária. Aviso do link MS acima:
If your destination table contains a primary key, make sure you append unique, non-Null values to the primary key field or fields; if you do not, the Microsoft Access database engine will not append the records.