Legislation is not law w/o both houses concurring. Boehner is seeking the right to sue the President which requires a change in the law affecting the relationship between 2 branches of government.
Constitution, Article 1, section 7:
Every Bill which shall have passed the House of Representatives and the Senate, shall, before it become a law, be presented to the President of the United States: If he approve he shall sign it, but if not he shall return it, with his Objections to that House in which it shall have originated, who shall enter the Objections at large on their Journal, and proceed to reconsider it........
They are not passing a law ... they want to have “standing” as a “body” (the body being the US House of Representatives) ... therefore the vote being passed by the House shows that the court case is from “that body” - the US House of Representatives.