Let's start trivially: The leds don't have current limiting resistors anymore.
Every electronic engineer worth it's salt looks funny at a construction like
that if he hasn't seen it before: haven't we all been taught you can't drive
a led without a current limiting resistor? Some research indicates this is a
completely valid thing to do in this situation, though. Allow me to explain:
The ATTiny13 datasheet states the maximum current through it's IO-pins is
40mA. Go beyond that and the device is toast, at least theoretically. What
is the maximum current that can flow when we directly connect a LED to the
IO-pin? There's a small graph in the datasheet that'll give us that info:
At a supply voltage of about 2.7V (remember, the schematic is powered from 3V, which is close enough) and an IO-pin voltage of 1.5V (the voltage drop of a normal LED), the current is limited to 15 to 20mA. That is exactly what we need.
As we can see, in this case we can safely remove the current limiting resistor. If you want to use this trick yourself, however, take a good look at the datasheet: this little trick won't work if you, for example, use 5V to feed the AVR.