I looked up some Radeon 9550 cards and they normally didn't have auxiliary power connectors on them. However, they also didn't have the key to support a 3.3v slot, and yours does. This is an odd card.
I noticed on NewEgg the Powercolor 9550 R96-LC3 was more conventional, 128MB 128bit, 250MHz GPU, no power connector and only had the 0.8v/1.5v key.
The Powercolor 9550 R96-LD3 looks like yours. 256MB 128bit, 250MHz GPU, with power connector and dual keyed.
I don't see why they would have needed extra power if those specs are accurate, and the heatsink certainly doesn't look like a lot of power is being consumed. But it would be safer to plug it in.
As Standard Def mentioned, all I can think of is that maybe they were worried about early AGP motherboards (which maybe they were trying to support with the extra key on the connector).
Some early AGP motherboards (generally those that used an AT power supply) weren't capable of providing as much current through the AGP slot as the standard required, so at least with those motherboards I'd definitely use the molex.