The basic idea behind the ruling you're looking at is that when a player asked to make a choice, they cannot choose an option that's illegal or impossible to perform. (For those following along at home, see CR608.2d for full details. As usual there's a few exceptions, but none of them apply here so we'll gloss over them.)
If you control a
Narset, Parter of Veils and your opponent hits you with a creature that has a
Mask of Memory attached to it (for example)–the Mask gives them a choice between “Draw two cards” or “Do nothing”. Sure, other things might happen later on depending on what choice is made, but that doesn't matter–the actual choice being made is still just between those two options. Well, thanks to Narset, drawing two cards is impossible, so your opponent is forced to choose “Do nothing”. So that's what they do, and nothing happens.
Risk Factor works differently, because it's offering a different choice. When your opponent's Risk Factor resolves, it gives you a choice between “Risk Factor deals 4 damage to me” or “Not doing that”–that's all. (Sure, other things might happen later depending on what choice is made, but again, the actual choice is only between those two options.) Nothing about Narset prevents you from choosing to have a spell deal damage to yo, so you can choose whichever of the two options you prefer. And once you make your choice, the rest of the spell resolves and does whatever it can. If you chose not to take the damage, Risk Factor tries to get your opponent to draw cards…but can only make them draw one. Oh well,
c'est la vie, let's all move on with the rest of the game.
It doesn't matter which player is being asked to make the choice–all that matters is whether or not the choice being made is possible. So yes, the situation would change if the choice being made was whether or not the player draws cards–if in your example your opponent put a
Combustible Gearhulk onto the battlefield instead of playing
Risk Factor, you could not choose to have them draw cards and would therefore definitely end up taking a bunch of damage.