One impact is how Kuwait was used for power in the Gulf States. It was the only "pro-soviet state in the Persian Gulf. Kuwait acted as a conduit for the Soviets to the other Gulf States. It was also used to demonstrate the benefits of a pro-soviet stance.
Another impact are the views Russia and Kuwait have. They have similar views on foregin policy issues. They both agree on the Arab-Israeli conflict. Also, the Soviets supported Kuwait's nationalization of its oil.
Iraq's territorial issues with Kuwait was another impact. Russia and Iraq had a very strong relationship, until the overthrow of Abd al-Karim Qasim. This ruined their relationship. However, it did help the relationship with Kuwait.