Is it true that a truly happy person doesn't have any malice towards others?
Completely true.
But I wouldn’t mix gossip and malice. Gossip by itself does not amount to malice (unless, of course, it’s malicious).
Yes, in complete, absolute happiness all ill-will towards others disappears. It does not mean you would not protect yourself against their ill-will towards you (for example, if they want to beat you), but you would not experience any emotional reaction to their behavior, such as anger, hate, contempt, jealousy, emotional pain, or hurt feelings. You would also not be able to get offended or hold a grudge. In order to get rid of ill-will towards others one has to first get rid of all ill-will towards oneself, which means accepting oneself fully and unconditionally. Paradoxically, this includes first accepting and not judging yourself for all malice and ill-will towards others which is presently there.
Such state of absolute, complete happiness is exceptionally rare and basically amounts to what is traditionally known and described as “spiritual enlightenment”. It is a state of infinite self-love and self-acceptance which results in the ability to be unconditionally accepting of others.