If the first major consequence of the First orbital war was speeding up long term and long range space operations by the superpowers, the second was clearly the initial LEO treaty that was negotiated as a result of the war.
Before the war, the civilian benefits of satellite/orbital technology had been obvious, and exploitation of this potential was a major goal of both private industries and the non-aligned developing nations (Argentina, Brazil, India, South Africa). While only a few private or Non-aligned powers had lofted satellites, the Orbit war destroyed them all by direct attack, or as a consequence of other attacks.
Both the run up to the war and the result of the war was an almost complete degredation of orbital infrastructure: in short, no sooner was a satellite lofted than it was destroyed.
As most space exploitation was military, anything in orbit was potentially a weapon. Indeed, the main casus bellum for the war was the “neutralization” of a large scientific satellite that proved to be an nuclear platform (from debris analysis); that it was also manned was the stated issue, but both sides knew that the lesson of project Prometheus was that gaining nuclear high ground was decisive. Once nuclear weapons were potentially in orbit, no satellite could be trusted. Unfortunately, as previously discussed the operations required to control LEO had exhausted both sides resources and personel and was unsustainable, and simultaneously unavoidable.
The desire for both of the superpowers to disengage from active orbital fighting coupled with the non-aligned powers desire to have an orbital infrastructure to create the the 1959 LEO treaty. In its simplest form, the LEO treaty declared that non-military satellites and operations were off limits to attack, but were also completely open to inspection and verification. Military operations were unaffected, but made responsible for collateral damage. Secondarily, the UN was tasked to undertake enforcement, inspection and orbital cleanup, a duty vested in the UNPAX forces patrolling the Eurasian DMZ areas.
Many historians mark the beginning of the estrangement of both the USA and the USSR from the UN, although the 1957 relocation of the UN headquarters into the BENELUX Mandate is also significant. Regardless of the cause, the LEO treaty clearly showed that by unified pressure (economic and political) the non-aligned powers could dictate some terms to the superpowers; increasingly, the UN became the vehicle for such action. A bipolar world was beginning to evolve into a tripartite world.