Right, RAPL just reports a total power usage figure for the whole CPU. The authors then develop a model which they believe splits that total into multiple components that correspond to parts of the CPU. This is possible because CPUs provide performance counters that measure what the CPU is actually doing. For example if you write programs that are very similar but have different ratios of cache hits and misses then they’ll draw different amounts of power. You can use those differences to devise a formula for the amount of power used by the cache.

And indeed, they give their formula in section 4.2:

    P_package = 6.05 + cycles/second × 1.63×10⁻⁹
                     + μops issued/second × 2.15×10⁻¹⁰
                     + μops decoded/second × 1.40×10⁻¹⁰
                     + L1 hits/second × 4.35×10⁻¹⁰
                     + L2 references/second × 4.05×10⁻⁹

You can see that the power used by the whole package is the sum of six terms. The values that the calculated for those six terms for each of their benchmarks are given in table 4. The 22W figure for the core(s) is just based on the frequency the CPU is running at.