Nah, he's about right. Duck hunt is bar none the worst character in the game at killing by a fair margin, and with the goal of the game being to kill your opponent... That puts him pretty far down overall. He has some quirks, but nothing that comes even close to matching that weakness.
I take issue with your statement about Duck Hunt being the worst at killing by a fair margin when Game & Watch exists. Now, my skill with Duck Hunt is pretty low. And he does seem to have significant problems killing. I won't directly refute your claim and say Game & Watch is the worst at killing because I feel that's a hard assessment to accurately make. But I'd like to bring some points up for discussion.
Game & Watch has one of the slowest starting sets of smash attacks in the game. Duck Hunt's smashes are unreliable at connecting (which is a DEFINITE hindrance) but their startup is respectable at 12, 7, and 7 for side, up, and down respectably. Game & Watch is working with frame 17, 24, and 15 smashes. FSmash and DSmash have good reach but can be tricky to sweetspot, and USmash is notable for being the third slowest move of its kind after Lucas and Ike and lacks their range and power. In fact, its hitbox size is positively tiny and doesn't even reach behind his head. The move has some nifty invincibility frames to help compensate, though, so I can't complain too much (I actually think the move is pretty well designed aside from its two-sizes-too-small hitbox). Just pointing out that you definitely have speed on your side here.
Neither character's aerials are particularly powerful for KOing aside from UAir. Game & Watch has a slight power advantage here but the attack is extremely finicky and hard to link both hits at kill percents (instead of the autolink angle the first hit has knockback growth). Duck Hunt's is superior in this regard. DThrow to UAir can be a kill combo but its effective percents are limited and the combo can be DIed making followup nearly impossible.
Both character's projectiles can set up for a kill but this is usually unreliable. At least Trick Shot has outright KOing ability.
Duck Hunt has a definite weight advantage. I despise dying at 60% when my opponent is at 150% and I can't properly land a move that will kill (rage is infuriating). But Game & Watch's recovery is 100% superior to Duck Hunt's making gimps a far less likely possibility.
Game & Watch does have one last-ditch kill move that is decent: DTilt. It does a measly 6% but hits on frame 6 and has significant knockback growth (pretty much the only meaningful buff he's received). It'll kill around 120% at the ledge. Not sure if Duck Hunt has anything like that.
Duck Hunt gains exponentially more from customs than Game & Watch and far superior traps. As far as securing kills go, both Fire customs represent a notable power increase. The first guts his recovery noticeably, though, and the second lacks a hitbox during the ascent (though the initial launcher hitbox when sweetspotted kills around 120%). Haven't played enough with the moves to see how useful they'd be; the default is amazingly versatile but if kills can be secured more readily it may be worth forgoing.
Game & Watch's kill potential feels frustratingly balanced around Oil Panic and Judge, which are both OHKOs or close to it. It's far easier (and safer!) to fill the bucket in FFAs and random Judge pulls fit better in that circumstance too.
IIRC you play with Tweek so you probably know better than me but Bowser Jr.'s killing ability also feels very substandard to me.