Connecting game system to pc monitor help

not really a computer question i guess, but sorta is.

short story:
does putting an adapter from a composite connection to an s-video connection upgrade the quality to s-video, or does it stay as composite quality?

long story:
i want to play metroid prime 2 for gamecube on my computer during breaks. i connected the red and white cables to the light blue input on my computer, and the yellow composite cable to the composite input on my 2005fpw dell monitor. it works, but looks kinda crappy. like, it’s not crisp, it looks jaggedy.

a few months ago my friend hooked up his gamecube to my monitor and i started my metroid prime 2 mission and it looked absolutely perfect. he took it back like a week later and i just remembered to bring my cube in now, but i forgot how we connected it before to get that crisp picture. i know he connected it with his own cables, but he forgot how we did it too.

my question is, if i get an adapter like the one below and plug the yellow composite cable to one end, and then the other end of the adapter to the s-video input on my monitor, will that give me s-video quality, or will it still be composite quality? like, i suppose you could downgrade your s-video quality to composite, but could you upgrade your composite wire quality to s-video quality just by adding an adapter like the one below?