The question is a tough one because it is very hard to know what Camus had in his mind while writing that. Many interpretations are possible. However, there is one way to look into it.
Camus starts from presupposition that life is absurd and meaningless. This is important to remember. Camus also considers the philosophers that mitigate or eliminate the absurdity by turning to other concepts as having failed in the task - the task of presenting an absurdist's actual point of view accurately. The moment you try to somehow answer to life's absurdity (which according to Camus is a conflict between reason and unreasonable) by abandoning or elevating reason, you have just compromised on the absurdist's position/feelings.
Sisyphus represents thus an ideal absurdist - one that has not failed like others. This is because he knows that he will never fulfill his goal and he accepts that. Thus, he is content - in a sense that he knows there is no life that is better than his that he should aspire because that is not possible (just like it is not possible for humans to have a better life though they might have more options than Sisyphus).
However, according to Camus, after acceptance of the absurdity (that absurdity exists), it is important to live it without abandoning it and falling in some kind of hope. Sisyphus does that. And, that makes him happy. Sisyphus is happy because he has conquered his fate - not by changing it, but by accepting it and yet revolting against it. There is no fate that cannot be surmounted by scorn. He is not saddened by lack of meaning and hence he is happy because he realises that.
Now, for answer to latter part of your question, consider the chain of events.
A man who realises that there is absurdity in life, that there is a conflict between what he thinks to be rational (should be) and how the world is, is saddened by this knowledge. What Camus offers is a solution that arises from making peace with fate (with disdain). A man must accept that the world is unreasonable and that he looks for reason and thus there will always be a conflict between the two. Now, when he accepts that, he is no longer sad. Because the only reason (in this context) for unhappiness is removed, a man is now happy. Here, I must give you an example -
You work in a 9 to 5 job and are happy. Suddenly you suffer the crisis that Camus is talking about. You realise that all this is meaningless. Getting up, going to office, succeeding some times and failing other times, coming back home, spending time with wife and children, going back to sleep, waking up next day again and so on. This realisation makes you sad. If somehow that sadness will be removed, you will be happy once again.
If Sisyphus dislikes pushing rocks, he will be never happy with it. But, if he is sad just because he knows he will never make it to the top, then if this only reason for his unhappiness is taken care of, he will be happy again.
You don't hope for a greater meaning or purpose. How does this make someone happy?
You may be happy in doing anything like rolling in sand, putting hands in a sack of grains, dancing impromptu, or putting ice cubes on your tongue. If you read Camus, you will see his characters get pleasure in all the things that somehow stir our emotions and make us happy - like lust for power etc. You become sad if you realise how meaningless they are or how they are immoral. However, if you accept that and accept that there is nothing better possible, and accept your fate (with disdain), then you will grow out of your search of trying to find a non-existent meaning. If you disregard there is something "better", that there are values, you will be out of the moral-immoral conflict in your head. And, thus you will be happy.
An absurdist is like a person who ignores that he will die one day ((ignores that life is meaningless) except that absurdist knows, accepts and does not ignore that he will die one day.
Consider Don Juan. He moves from one woman to next. He does not desire true love. He just wants to get most enjoyment from present moment. He knows the limitations. He knows that he won't get true love and he does not want it. The only happiness he has is the happiness that he experiences because of his acts. He does not hate what he does and what he does tickles his "happiness-inducing" senses. Hence there is no guilt but just petty happiness and it is all that he wants.
Whether this position can actually be defended and absurdist view can be held consistently is beyond the topic as Camus does not talk about that (whether Don will be one day realise how much better true love is and regret his actions), however, what is certain is that people do find happiness in acts that do not make a whole lot of sense - you might have seen those duck-faced selfies;)