A new chapter in the high-stakes, high-level political game of office building development in Washington is about to be written on the east side of McPherson Square.

Two big buildings, one to be built on land owned by the United Mine Workers of America and the other over the Metro station at 14th and I streets NW, are planned by partnerships that include all the "right" people for getting things done in D.C.

The mine workers have recruited builder Nathan Landow to advise them on how to develop their land on the orth side of I Street between 14th and 15th. Landow, one of the Carter White House's favorite fundraisers, must have looked to the union's president, Sam Church Jr., as the right man for the $18 million project.

Landow has become more and more plugged in with the city's political chief since he formed a partnership in 1978 with D.C. bond lawyer James L. Hudson, Willie Leftwich and Chester Davenport to build a portion of the Metro Center. More recently, Landow added another political figure to that partnership: D.C. Democratic chairman Robert B. Washington Jr.

Landow also was sponsored by Church as the newest member of the board at the National Bank of Washington, whose majority stockholder is the mine worker's union.

On the other side of the street, Metro officials have negotiated a lease for the "air rights" to build over the McPherson Square station entrace at 14th and I streets NW. The Partnership formed to develop that site includes banker and mayoral confidant William B. Fitigerald, real estate lawyer R. Robert Linowes, architect Arthur Cotton Moore, developer Melvin Lenkin and business consultant Larry Goodwin.

Fitzgerald and Goodwin were brought into the deal, one partner said, to satisfy the District's unwritten rule that members of minorities must be included as partners in office developments supervised by government agencies. Both Fitzgerald and Linowes are considered heavyweights in D.C. political circles. Fitzgerald is a poker partner, adviser and companion of Barry's. Effi Barry, the Mayor's wife, sits on the board of Fitzgerald's Independence Federal Savings & Loan.

Fitzgerald and a group of black bankers last year won the development rights to the city's last major downtown urban renewal tract, near the National Portrait Gallery.

Linowes, former president of the Greater Washington Board of Trade occasionally advises the mayor privately and serves as a liaison to Washington's business establishment.

The newly ambitious District of Columbia Development Corp. (DCDC) has developed some serious cracks in its foundations with the resignation of its president and several key board members.

A central issue, according to insiders who asked not to be named, is the operating style of DCDC chairman James R. Haynes, a gruff and sometimes feisty real estate lawyer who has clamped down on public access to the agency, which receives most of its money from the District and federal governments.

DCDC president Joseph D. Jackson resigned, effective Aug. 18, without having a new position lined up. He reportedly was furious with Haynes for instructing him to refer all public queries about DCDC business to Haynes, and for making decisions without consultant Jackson.

Jackson's resignation followed that of Joseph Carter, a Garfinckel's vice president who several months ago refused to sign a $40,000 check that was the first installment on the District's bail-out of Harambee House Hotel.

Longtime board member Frederick B. Abramson, of the law firm of Sachs, Greenebaum & Taylor, also has quit. Abramson said DCDC was taking up too much of his time, but he reportedly was very upset over Jackson's resignation. The third board member to resign was Annie Woodridge.

DCDC is facing a number of serious financial challenges, and Jackson's resignation leaves no one in the tiny agency who has had experience with both housing and commercial development.

Much of the recent pressure in the agency has stemmed from the financial rescue of Harambee House, which was built by flamboyant restaurateur Ed Murphy with the help of the Economic Development Administration.

The bail-out is a sensitive issue because city Planning Director James O. Gibson was one of Harambee's original backers.