Then uninstall the Unity web player browser plugin and never be bothered with running a Unity game again.
Doesn't seem that difficult.
And it's very possible Unity (or Flash or Java or JavaScript or ...) can give you a virus if someone found a means to exploit it, and software exploits are rampant, so I wouldn't discount that part of this guy's story right off the bat. And if there is a Unity game with a virus then Newgrounds should definitely be made aware of exactly which game it is so it can be removed. Unfortunately OP is no help here.