It would help if the people who say this scene made them laugh would actually go into detail about what it is that doesn't work about it. A few do in some places (like how oversized Dom's pistol is compared to a normally sized human in this universe), but for the most part, people aren't actually going into the why of the scene breaks down.
And if it's just that this is gears and they are constitutionally incapable of getting real pathos out of Gears, then... I mean, I guess, but that's still not a very strong argument. Lots of franchises have silly elements to them, it's like saying you can't take LotR's depictions of the horrors of war seriously because you can't get over how funny looking hobbits are. Or, to be more game related, no one would say that MGS's emotional moments are impossible to take seriously because the maincharacter hides from his enemies in a cardboard box. If you want to tell me how the scene broke down, actually tell me how the scene broke down.
For my part, I watched this when I was 18, in the context of the game, I found it to be emotionally effective, though it is an example of fridging. Today, the biggest issue I have with it is it's pretty explicit support and justification for euthanasia. Like, it didn't even occur to Dom to see if there was any way he could help his wife. Maybe there wasn't, but it's not like he's a doctor. Instead, it's just an immediate bullet to the head. Like, it's not even that euthanasia isn't philosophically justifiable in hyper extreme cases like that, but it's flippant depiction just seems a bit more uncomfortable than it is now.