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Yes, that's how it works. That network is commonly described as a diplexer although I can see why it may seem unconventional to call it a diplexer.
The energy from the mixer gets shared/split between the 50R load resistors and the spectrum analyser. At large frequency offsets (far away from 10.7MHz) pretty much all the RF energy from the mixer ends up as heat in the first 50R resistor. So in this sense this resistor is the other port that soaks up energy at the image frequency and at the leaked LO frequency. There probably is a better (correct?) name for this network but it has always been called a diplexer at work and it is often described as a diplexer in amateur radio literature.
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I see, cheers. Your C1 and L1 have the resonance reactance of 181.34 ohms and C2 and C2 reactance of 15.824 ohms. It works like a bridge tee attenuator that maintains 50 ohms for source and load input impedance to attain the design attenuator.