Isn’t the intelligence shown by compressing lossless the scheme you use? Applying the algorithm is the easy part, the proof of intelligence is inventing the algorithm which compresses.

Yes, you are proving intelligence if you invent the algorithm which compresses. If the prize was for inventing an algorithm that could then build the lossless compression scheme itself then you'd be onto something. But the prize is for the human who invents the better compression algorithm and proof of intelligence of the human would be self-evident.

Hutter put up the prize as a way of getting people to approximate his AIXI algorithm, which he already considers to be the pinnacle of artificially intelligence. That's also why lossy compression isn't interesting. It'd be an approximation of an approximation and not particularly useful for hutter's purpose.