That *might* work; however a much better (and more likely to work) approach is to get something off of a FM/AM stereo tuner. Many of these have an AM loop antenna that goes to a little black box, then is connected to the tuner. That little black box is what you want
It would take a considerable amount of explanation as to why - in fact, my old theory textbook has 3 chapters devoted to the subject - so at the risk of HIGHLY oversimplifying the issue, here goes nothing. Your loop is presenting a balanced load through those wires. (You can tell this by examining the wires - they're identical in every detail). It's likely someplace around 5 kohm or so. Your SDR expects a coax type load, which is typically 50-75 ohms or so (that's dependent on the SDR itself, I'm broadly generalizing here). So as you can see, we have a significant mismatch. Under such conditions. very little RF will flow. We need a transformer to go from a BALanced load to an UNbalanced load. Such a device is called a BALUN. The one in your pic might work, but it's more intended for use with antennas with a twin lead lead in or a single wire. It MAY work if the loop is presenting a load of around 450 ohms or so (which I doubt, frankly, but it's possible). It also might work if the antenna connection on the SDR is a bit more forgiving.
Still I think the balun from the AM loop antenna from a stereo tuner is much more likely to give better results. However the only thing you'll damage with trying what you've shown is your wallet if it doesn't work
Mike