I've just finished watching the first season of Arrow and noticed this too. I tried some online research, but I've come up empty, so here's my highly subjective speculation on the issue.
It's a possible mistake. The producers just didn't notice. This is unlikely, but it is possible. I remember watching an episode of CSI New York where the detective handled all the weapons in lock up that they'd taken off the suspect without gloves. A colossal no-no and one that any mild watcher of the show noticed. Yet amazingly the producers didn't. Still, I think this is unlikely.
It was a deliberate omission designed to show the boundaries between Oliver Queen the billionaire and Oliver Queen the arrow had been temporarily removed. There were no secrets between Malcolm and Oliver. They knew each other. Malcolm was fully aware of Oliver's exploits and Oliver had discovered the true identity of the Black Archer. Given these circumstances, the lack of eye paint could symbolise him going into the fight as himself. Remember the circumstances leading up to the fight as well. Malcolm had beaten him a few times and told him it was because he didn't know what he was fighting for. When Oliver showed up for the final fight, he was himself and he was fighting for what he believed in. His courage and conviction took him over the line.
There doesn't appear to be a definitive answer on this, but the second point above is my subjective take on the issue.