Certainly open source. The source is there. In the open. You're just not allowed to reuse it in the ways that we have come to expect from free software. So it's open, but not free, software.

The OSI definition for open source includes the right to use, modify, and redistribute it.

Of course, not everyone necessarily agrees with that definition, but one would typically use the term "source-available" for code that is publicly available with restrictions.

No, that makes it "source available". Not "open source".