For practical purposes, yes
Ice knife was errataed to not use language about a radius any more1, so it only cares about distance from creature to creature. That means that any creature within five feet of the target creature will be affected, just as the spell says. With a larger creature, you will affect a larger area.
How that translates in play depends on if you play on a square grid or not. If you do, then even though the creature does not fill the entire grid cell, any adjacent square will be in range, as the rules advise you to count that as 5 feet (p. 192 PHB):
To determine the range on a grid between two things — whether creatures or objects — start counting squares from a square adjacent to one of them and stop counting in the space of the other one.
As Dale points out, in the unusual case that you deal with 3-D combat, you will affect a larger volume, and also hit the cubes above and below the target creature2.
If you don't use a grid but still use miniatures, then you measure the distance between the creatures. If you use narrative combat, the DM will determine which creatures are within five feet of the target.
1 There is some discussion if effects that spread in a radius around a target creature (typcially the caster, such as Spirit Guardians around the caster or the effects of a scroll of protection) originate from the overall creature or a point you need to pick. This is not unequivocal, so it will require a DM call (strong majority vote on this site is that it will originate from the overall area the creature occupies). Because ice knife does not use the radius language, it avoids these issues.
2 If the target was Huge, then you would affect an area of 25 tiles or 125 cubes, and if it was Gargantuan, you would affect 36 tiles or 216 cubes.