Sadly, it isn't that simple. Basically what happened is that the Senate passed a bill (62-37) that coupled the Trade Promotion Authority (TPA) extension with an amendment that extended a worker retraining program. In the House the bills were decoupled. The vote rejected the *retraining* bill (but passed the TPA bill) which effectively requires a revote by the senate to grant TPA separately (if the goal is to get it in a form for the president to sign it rather than just blame someone for its failure to pass).
The extension alluded to by the OP is that there is an extension clause in the bill that allows the president to request an extension from 2018 to 2021, but the extension must be requested before June 30, 2018. If either house can pass a bill that rejects this extension, it is considered denied. FWIW, a similar extension clause has been in most TPA that have been granted in the past and were generally put in as a safety in case negotiations schedules are not maintained.
The only foreseeable situation that this affects is if one party were in control of both houses and the presidency, the out-party could then still theoretically filibuster a vote on a negotiated treaty in the Senate if the TPA authority was not in effect. However, with the recent change in filibuster rules of the senate regarding nominations by the democrats (the so-called 'nuclear-option' that was exercised), it isn't inconceivable that filibustering a treaty could trigger a similar 'nuclear' option in the senate if it came down to it, so it may not even matter in practice and is kind of a red herring.
As to why TPA is necessary, it of course isn't, but not having it allows a few members of congress to essentially hold the enabling legislation for a treaty hostage by offering amendments or failing to issue a committee report to allow a floor vote. Since adding an amendment would force the negotiators back to the table, it is presumed that other treaty parties would never offer their best level of concessions during ordinary negotiations (saving them to counter future nit-picking terms offered by rouge legislators) resulting in a sub-optimal agreement for us.
The TPA isn't like the war powers resolution in that it is a bill that affects the rules congress applies to itself by simply limiting debate, amendments and other procedural measures (which it is of course free to do to itself and has done many times in the past). The WPR is hotly debated as being unconstitutional in that it appears allows the president to take unilateral action and report on it later without action from congress. Also, the TPA also has many provisions in it directs negotiations a certain way and if the president ignores them, the TPA is effectively revoked (debate and amendments are then allowed in these areas). Unlike the WPR, the TPA allows congress to reject a treaty *before* it takes effect (not after the fact like the WPR).