Is a Winchester repeater a rifle?

Yes or no, depending on what you are really asking. This question is poorly phrased.

Winchester is a company which makes guns.

A "repeater" is any gun which can be shot multiple times before it is necessary to reload it.

A rifle is a long gun which shoots a single projectile for each shot, as oppposed to a shotgun, which is a long gun which shoots small, multiple projectiles for each shot.

Winchester has made several rifles and shotguns which are repeaters and they have made several rifles and shotguns which are single shot (i.e. not repeaters).

The answer is then that a Winchester repeater could be either a rifle or a shotgun.