LIV Golf, which is backed by Saudi Arabia's Public Investment Fund, submitted an application to the Official World Golf Ranking (OWGR) board in July and earlier this month formed an alliance with the MENA Tour in a bid to fast-track its quest for ranking points.
The OWGR said it would make a decision after reviewing changes to the MENA Tour, prompting LIV golfers to say it was dragging its feet.
Two-time major winner Dustin Johnson clinched the individual title in the LIV event in Bangkok on Sunday and McDowell said failure to award him ranking points meant the two-time major winner was not in his proper spot.
"This guy standing in the middle of the three of us (Johnson), if his world ranking is inaccurate, then the whole system is inaccurate," McDowell told a news conference on Wednesday, speaking alongside Johnson and Harold Varner III.
"I feel like LIV tried to do everything they possibly can to be legitimate in the eyes of the OWGR.
"The word 'Official' has to go away from OWGR if they don't take care of the players out here."
Johnson, whose ranking has dropped to 24th from third at the end of 2021, pocketed $18 million after clinching the individual LIV title with a 16th-place finish in Bangkok.
LIV Golf has lured away some of the US-based PGA Tour's top members with huge sums of money, leading to a simmering feud between the sport's top players and organisers.
Players who compete in the breakaway series have been suspended from the PGA Tour.
Attempts of Europe's DP World Tour to follow suit have so far been unsuccessful with LIV players still eligible to compete at its showcase events pending a court hearing next year.
On Tuesday, former Masters champion Hideki Matsuyama said he was "fully committed" to the PGA Tour but thought golfers competing on the LIV should be eligible for ranking points.
LIV's individual competition concludes in Jeddah from October 14th-16th before a final team championship in Miami.
