TMS9918 datasheet, PDF page 80:
Nominal video output voltage levels specified for a 470 Ohm load:
Vwhite=3.0V, Vblack=2.3V, Vsync=2.0V.
Since monitors tend to have AC coupled video inputs, it isn't supposed to matter if there is a little DC bias voltage on the video signal.
The 2N4401 transistor works as an impedance converter for driving a 75 Ohm coaxial cable.
When a smaller video signal amplitude is needed, the Zero Ohm resistor can be replaced with another resistor for building a voltage divider.
From the datasheet, 2N4401 can drive up to 500mA.
Assuming a 0.65V voltage drop in the transistor, and a 75 Ohm termination resistor at the monitor input, the collector current would be
(3.0V - 0.65V) / (75Ohm || 75Ohm) = 63mA for white level,
(5.0V - 0.1V) / (75Ohm || 75Ohm) = 131mA for a short circuit between transistor base and VCC if the transistor goes into saturation.
2N4401: 500mA, 250MHz.
BC547: 100mA, 300MHz.
BC337: 800mA, 100MHz.
If you don't have a 2N4401 at hands, try using a BC337 instead, it's supposed to be fast enough.
If you don't have a 75 Ohm resistor at hands, use two 150 Ohm resistors in parallel instead.
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Composite video signal levels at wikipedia:
Hope, this helps.