No. Call that "source available", "source access" or something, but "Open Source" is pretty much established to be defined by the OSI definition of the term: https://opensource.org/osd
The OSI should trademark the phrase "open source". License it for anyone claiming their software is open source (as defined by OSI), and send cease and desists to anyone who is using the phase incorrectly.
We have discovered that there is virtually no chance that the U.S. Patent and Trademark Office would register the mark "open source"; the mark is too descriptive. Ironically, we were partly a victim of our own success in bringing the `open source' concept into the mainstream.
Open Source need not be free as in beer, nor as in freedom.