Why is a "field" on a form called a field?

My Glossary of Computing Terms: An Introduction (pub BCS, 1984) says

Field is a predetermined section of a record

which covers forms as well.

OED shows the origin is surprisingly early:

19. Computing. Any one of a number of places where a user is expected to enter a single item of a particular type of data; an item of such data; esp. one in a database record. Cf. data field n. at data n.

Originally a group of columns on a punched card.

1903 Jrnl. Polit. Econ. 11 372 The fields are to be punched in the regular order by touching the keys indicated from left to right.

Data field was apparently first mentioned in a patent:

data field n. a section of a record, esp. in a database, in which an item of data is entered; each of the particular types of data held in a database.

1929 Brit. Patent 302,314 9/9 A previous inventory perforated strip P1, the separate data fields of which give, inter alia, the following data [etc.].

It's a fairly small step to extend other earlier uses to reach the above meanings:

10. a. An enclosed or marked-out area [for playing sport]

or even

II. An area of operation or observation.
12. a. An area or sphere of action, enquiry, or interest; a (wider or narrower) range of opportunities, or of objects, for activity or consideration; a theme, a subject. Freq. with of.
b. As a mass noun: scope, opportunity; extent of material for some specified action or operation. Freq. with for.
c. A particular branch of study or area of expertise or competence; a subject. Also more fully field of study.

Not a big mental stretch to got from a "field of study" to a "field of data"