Why do you think Outer Space Treaty will matter in event of a hot war between two nuclear superpowers? NPT was signed a year earlier and it has been continuously violated by signatory powers to this day.
Your own source describes the idea that this was a program design goal as a "myth," and clarifies that it was born of a Soviet capabilities analysis suggesting that this theoretically could be done with the Shuttle, not that there existed any evidence that it was intended.
On the latter point you have your causation backward. The intent of treaties like the Outer Space Treaty was to reduce the likelihood of a hot war by interdicting the use of technologies that would destabilize the strategic balance.
Treaties work until they don't, and what can cause an escalation is future knowledge beyond our abilities to predict. In event of a hot war, none of these treaties would've mattered.
On the latter point you have your causation backward. The intent of treaties like the Outer Space Treaty was to reduce the likelihood of a hot war by interdicting the use of technologies that would destabilize the strategic balance.