No, it is not.

    3.195 Incomplete Line

    A sequence of one or more non-<newline> characters at the end of the file.

    3.206 Line

    A sequence of zero or more non-<newline> characters plus a terminating <newline> character.

courtesy of [0]. See also [1] for rationale on "text file":

   Text File

   [...] The definition of "text file" has caused controversy. The only difference between text and binary files is that text files have lines of less than {LINE_MAX} bytes, with no NUL characters, each terminated by a <newline>. The definition allows a file with a single <newline>, or a totally empty file, to be called a text file. If a file ends with an incomplete line it is not strictly a text file by this definition. [...]

[0] https://pubs.opengroup.org/onlinepubs/9699919799/basedefs/V1...

[1] https://pubs.opengroup.org/onlinepubs/9699919799/xrat/V4_xbd...

Applications that write "incomplete lines"

- VSCODE

- Visual Studio

- Notepad

C/C++ compilers that process "incomplete lines"

   All of them.

Will my users consider it a bug if my program doesn't process "incomplete lines":

    Yes. (Yes, I have had this bug logged 
    against code that I wrote).

Will I consider it a bug if your program doesn't process "incomplete lines":

    Yes.

> Applications that write "incomplete lines"

Note that all of those three apps come from the Windows world where CRLF was indeed a line separator, and a file ending with CRLF was considered to have an empty line at the end.

But yes, you absolutely should accommodate for incomplete lines.

Not everything uses POSIX maybe that's a reason for the different results.