This response is based on the information provided. We suggest you discuss with your contracting officer, financial manager and/or legal department as appropriate.
This question is related to the "Purpose Rule " which explains that monies can be used only for the purpose for which they were intended by Congress (and subsequently the offices the funds flowed through to get down to yours organization), i.e. if the intent of a particular set of funds was for travel, those funds generally could not be used for an addition to the office space.
Under the Purpose Statute, 31 U.S.C. § 1301, funds are available only for the purpose for which Congress appropriated them. Financial Management Regulation Volume 2, Chapter 3 discusses the three-step framework used when determining whether appropriations are available for a particular purpose. Sections of the chapter correspond to each step of this framework.
The expenditure must not be otherwise provided for, i.e., it must not be an item that falls within the scope of some other appropriation or statutory funding scheme.
Assuming the funds the unit has are operations and maintenance (OMA) funds, purchase of fitness equipment might be appropriate. But given the Army, the command, had already purchased fitness equipment, these funds likely should not be used for fitness equipment. The captain's unit will need to make the case as to why the fitness equipment already available does not meet mission needs, e.g. gym hours incompatible with unit mission, fitness equipment too far away from unit as examples.