It's not especially weak (beats the heck out of any 8-bit era system and can probably give Genesis a run for its money), but the CPU basically must do everything. There's no real graphics or sound hardware; the CPU must generate everything 100% in software, which burns up a lot of cycles (although Propeller has serialization and clocking features that make this less of a pain than it would be on e.g. an SX or PIC chip) . However this also has the advantage that you're not locked in to one particular model of graphics/sound.
Incidentally, if you have the ability/desire to actually build your own, it could be much cheaper than buying the Hydra kit. The actual Propeller CPU that does all the work costs about $13, and the rest is pretty much just the power supply circuitry, connectors, a simple resistor DAC, and a handful of other resistors/capacitors in usual roles. I think the Hydra has an FTDI USB-Serial chip on there as well, which costs around $5; if you can settle for a regular serial connection a MAX232 or similar chip could be used instead. Parallax freely offers the schematic of their own Propeller demo board with has both NTSC and VGA outputs, so that could be used as a reference...