It's a common-base amplifier, so the voltage gain is positive and can be greater than one (which of course is necessary to get more output swing from less input swing).
Current gain is less than one, so the 1.8V logic has to be able to sink the 3.3V logic pullup.
This is a saturating circuit, so the base supply has to be current-limited, and a speed-up cap is optional (although 1nF seems way too much -- 100pF would be enough for a 2N3904).
For greater output voltage swings, this circuit has the advantage that Miller effect is nearly eliminated. So you can go from a very low logic level (1.2V or more), up to a full voltage swing, which might include applications from gate drivers (10-30V swing) to nixie drivers or CRT blanking (50-200V swing).
Here's an example where I used a 1.2V logic level (set by D2 Vf + Q3 Vbe) into a common-base level shifter (Q4, D3, D4), with a current source pull-up for better speed (Q5, Q6 and such), then emitter follower for gate drive:
https://www.seventransistorlabs.com/Class_D_Amp.pdfIt works just fine with MOSFETs too, with the difference that the gate voltage bias and input swing need to be adequate for the part. A 2N7002 needs 2 or 3V (gate to VDD, source to low-level logic, drain to pull-up). A depletion type would have gate tied to GND instead, which means an open-collector/drain pin can drive it and it supplies its own pull-up through drain-source current (though a pull-up from source to VDD will speed things up a bit).
Tim