OK, it makes more sense now I've seen the article. The reason they are using 'forced beta value of 10' is to ensure the transistor is fully saturated (as conductive as it can be) but in reality you can probably relax that quite a lot as the Hfe (beta) of the transistor is likely to be much higher than minimum specification. The transistor is however, not suitable as you observed, you must use one rated at least to carry the motor current and preferably 50% - 100% more as the capacitor also draws current when the transistor is turned on. A small power transistor would be a better choice, or best of all, a logic level MOSFET.
Brian.