I would say that being a knife is totally secondary to being a multi-tool. (bladeless fuse?) but its the addition of other tools to a main tool for convenience, regardless of if it works or not. so those little combination knife/crescent wrenches, or fencing pliers (hammer pliers) are both multi-tools, one has a knife, and one doesn't (and guess which one actually works?) but if someone made a high quality crescent wrench knife, I would probably need one.
A better definition might be that a multi-tool is anything that has more than one obvious and dedicated tool with a discrete usage. So a knife can be used as a prybar, but is not a multi-tool, but a knife with a designed prying pommel would be.