I don't know what your local building code requires, but combustion and dilution air requirements are specified in the Fuel Gas Chapter (chapter 24) of the International Residential Code which forms the core of most statewide building codes.
You can use indoor air to meet the requirements for combustion and dilution air under G2407.5.1 of the IRC. The 50 cu. ft./1,000 BTU minimum volume would include the combined volume of the Rec Room and Mechanical Room since there are vents which allow the two spaces to communicate with each other.
You'll need to determine whether the "tight" construction of your home requires you to follow the calculation method prescribed in G2407.5.2 If your blower door test report indicates less than 0.4 ACH, the follow the prescribed calculation method in section G2407.5.2
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