You need the resistor to put enough load on the SCR to meet it's minimum holding current. If you look at the data sheets for MCR106 and 2N5060 you'll find that the requirements are basically the same so the AUX lamp driver should need them the same way the main lamp driver would. I've noticed that it's not consistent from game to game and the results won't even be exactly the same from SCR to SCR so it might not be as noticeable in some cases. The AUX lamp driver boards also use only the larger SCR which will drive multiple lamps in some cases which might draw enough current to eliminate flicker when driving multiple LEDs.

Ohms law tells us that 470Ω resistors are the closest to the minimum holding current while going slightly over, drawing approx 13 mA. 330Ω will draw only approx. 7mA more so not really a big deal either way, even if someone should install a #44 lamp at some point, but we only need to draw 10mA thought the SCR, according to the data sheet, to keep it on and the LED is going to draw at least a few mA on it's own. I've also seen people using as high as 1.5KΩ with success.

It's also going to be really dependent on which LEDs you use. The current draw will vary quite a bit. The brighter LEDs which draw more current might not even need the resistors. Based on the specs in the data sheet I would expect this to be the case with a lot of pinball LEDs, but it doesn't always work out like that in practice.

Data Sheets:
http://www.onsemi.com/pub_link/Collateral/MCR106-D.PDF
http://www.onsemi.com/pub_link/Collateral/2N5060-D.PDF