Why is that capacitor necessary?
Reduce electrical noise within the processor. The analog-to-digital converter in the ATmega328 processor, for example, is internally separated from the rest of the processor which helps to reduce interference from internal sources. The ATtiny processors are not structured that way so other measures, like a bypass capacitor, are, in my experience, more significant and more important.
I think it'll have one anyway with the 5v regulator.
You will not. The capacitors on the regulator serve a different purpose.
In case you have doubts, I refer you to the ATtiny85 datasheet...
17.9 Noise Canceling Techniques
• Place bypass capacitors as close to VCC and GND pins as possible.
A good system design with properly placed, external bypass capacitors does reduce the need for using ADC Noise Reduction Mode