Spellskite is not a legal target for the counterspell, so when the ability resolves it will not change the target, it would remain the same.

What can spellskite redirect?

It can only redirect spells or abilities which can legally target it. However, it can target any spell or ability. There is nothing wrong with your opponent paying 2 life to try and change the target of your Go for the Throat, then fail to. It can only redirect spells or abilities which can legally target it.

Can spellskite steal equipment?

As awesome as Spellskite can be, he can never convince the game that he's your opponent's creature (unless, of course, your opponent takes control of him). ... The Equip keyword means this: “Attach this equipment to target creature you control.