This statement is quite true. Neither side really did gain a major advantage from its involvement in this conflict.
The USSR backed the Arabs in their conflicts with the Israelis. This made Arab countries at least somewhat more friendly with the Soviets than with the Americans. However, these countries did not become Soviet satellites. Instead, the followed the lead of Egypt and tried to remain as fairly neutral parties in the Cold War, pursuing their own good and not that of the Soviet Union. The Soviets were not able, for example, to get their Arab allies to use their oil to harm the US.
At the same time, however, the US did not gain much from its support of Israel. It did gain the fairly firm friendship of the most powerful country in the Middle East. However, it did so at the price of damaging its relations with some Arab countries. Since the Arab countries were important due to their oil and their location, this damage was actually important.
Neither the US nor the USSR was really able to improve its overall global status or power as a result of involvement in this conflict.