"--install-types not supported in this mode of running mypy" even with `--non-interactive`

Bug Report

When running mypy with redirected stdout / stderr (for example, via mypy.api.run), --install-types fails with:

error: --install-types not supported in this mode of running mypy

Per the comment, this is because --install-types performs user input. However, when --non-interactive is specified, no user input is necessary, and this error should not be raised.

To Reproduce

1. Create a file src/foo.py like:

# src/foo.py
from mypy.api import run

_, _, exit_code = run(["--install-types", "--non-interactive", "src"])
assert exit_code == 0

2. Run python src/foo.py

Expected Behavior

The program exits with exit code 0.

Actual Behavior

Traceback (most recent call last):
  File "src/foo.py", line 4, in <module>
    assert exit_code == 0
AssertionError

Your Environment

• Mypy version used: 0.910
• Mypy command-line flags: --install-types --non-interactive src (invoked via api)
• Mypy configuration options from mypy.ini (and other config files): N/A
• Python version used: Python 3.7.5
• Operating system and version: Ubuntu 18.04.5 LTS (Bionic Beaver)

Start by inspecting the --install-types mode check in mypy/main.py and reproduce the failure through mypy.api.run using --non-interactive. Done means this invocation no longer reports that the mode is unsupported and exits with code 0.