It's a complicated question because between those two time periods you're really talking about two fundamentally different systems of oil production.

In the early 1950s, generally speaking, Middle Eastern oil production was controlled by foreign-owned oil companies like the Anglo-Persian Oil Company (renamed to its more familiar moniker British Petroleum in 1954, and now just "BP".)

These companies, many of which were owned in whole or in part by foreign governments, set the price of oil very low: cents per barrel.

In the early 1950s some of the largest oil fields in the Middle East also hadn't yet been discovered or were just coming on line. So for example the UAE's oil fields weren't discovered until the late 1950s, and some countries like Saudi Arabia that already had oil were making large oil discoveries at this time.

The 1950s and 60s saw the emergence of nationalization and cartel-ization of Middle Eastern oil. Famously in 1953 the CIA helped launch a coup in Iran in part because Mossadegh was threatening to nationalize Iran's oil company and raise prices. While that coup was successful, the overall efforts to stem the tide of nationalization and price increases was not. OPEC was founded in 1960, critically with the inclusion of Venezuela in the cartel.

In the context of the meeting you were reading about, Egypt has never been a significant oil producer. But, oil is critical to the revenue of the Suez Canal, as oil tankers make up a very large percentage of the ships that transit the canal and the tolls that those ships pay made up then (as now) about half of the known revenue of the Egyptian Government.

The discussion you cited, in 1953, was part of discussions about what kind of control and force presence the British would have in the Suez zone going forward. In 1956, Nasser nationalized the canal entirely, precipitating the Suez crisis. In this context, even though Egypt was not an oil producer, it can be viewed as part of this wave of oil-related nationalizations.

Between the 1950s and 1970s, US oil imports overall also increased dramatically as you can see from some of the charts here: https://www.eia.gov/energyexplained/oil-and-petroleum-products/imports-and-exports.php

But overall, Persian Gulf oil was still a small fraction of overall US oil imports. What had changed was that these countries now controlled a larger share of global oil production and that the oil market itself had been dramatically affected by price increases, nationalization, and cartelization.

Had those conditions existed in 1953, I'm not so sure that Dulles would have been so cavalier about oil reliance, because the ability to shock the oil markets was probably already in place given their share of global production and the emphasis that the US placed on maintaining the status quo as exemplified by the Iranian coup.

For more on the specific Egyptian context see Mike Doran's Ike's Gamble. On this general process of nationalization, see, for example, the relevant chapters of Eugene Rogan's The Arabs: A History.