The constructor for the SoftwareSerial object expects to be given both a TX and and RX pin (and, optionally, a boolean value representing whether or not it should use inverse logic.) From SoftwareSerial.h, see:
SoftwareSerial(uint8_t receivePin, uint8_t transmitPin, bool inverse_logic = false);
If you want to use the library in the way you've written, you'll need to either modify the existing constructor or write a new one into the library.
As a quick test, I've added the following lines to each of the listed source files:
SoftwareSerial(uint8_t receivePin, bool inverse_logic = false);
SoftwareSerial::SoftwareSerial(uint8_t receivePin, bool inverse_logic /* = false */) :
Now there's a constructor that allows for a single RX pin argument like you've outlined in your initial example. The problem is that this is likely to break anytime the Arduino codebase gets updated and your changes get blown away.
Best practice may dictate writing your own driver to use the serial functionality of your ATTiny without the possibility of accidentally using the TX functions, but if this is a one-off then maybe Bence Kaulics' suggestion of just feeding it a nonsense pin would be the least time-consuming.