I'll give my interpretation, but since Nietzsche wrote in German, I use the German text.
Über sich selber lachen, wie man lachen müßte, um aus der ganzen Wahrheit heraus zu lachen, dazu hatten bisher die Besten nicht genug Wahrheitssinn und die Begabtesten viel zu wenig Genie! Es gibt vielleicht auch für das Lachen noch eine Zukunft! Dann, wenn der Satz »die Art ist alles, einer ist immer keiner« – sich der Menschheit einverleibt hat und jedem jederzeit der Zugang zu dieser letzten Befreiung und Unverantwortlichkeit offensteht. Vielleicht wird sich dann das Lachen mit der Weisheit verbündet haben, vielleicht gibt es dann nur noch »fröhliche Wissenschaft«.
It is worth nothing, that this is a small passage which is named (in English)
The teachers of the purpose of existence
It also may be relevant for English readers, that at least in German
to laugh out of the whole truth could be read as the double-meaning to laugh yourself out of the truth (like "laugh the truth away") and to laugh from within the truth (as in truth transcends you). At least that's what the rest of the text would seem to imply.
One could read the entire thing as a rant against purpose and specifically those who seek, preach and strive for it. But I have a strong suspicion, that this wouldn't be quite what he is saying. Rather this: the sentiment
the species is everything, one is always none is so obviously true throughout history and across all schools of ideas, that it could be laugh-able (in the sense of how one could laugh mentioned above), but it is not (yet), because nobody gets it, not those who claim it and not those who claim the opposite or anything else really.
You could understand that as a rant against the very idea of any other purpose of being there, than just being there and that's not wrong. But it also sounds truly passionate, dreamy, almost hoping that one day the members of species as a whole would be capable accepting (no: embracing - no: joyfully celebrating) themselves as unimportant and that this liberation would bring with it the end of the necessary cruelty and idiocy that lays in the eager search of purpose and the beginning of untainted, joyful exploration.
Or - in a sloppy tl;dr style I'd translate it into:
Chillax, there is no you in we and isn't the ridiculousness of us and everything the best thing ever? Right, so we could just enjoy this incredible reality of our species as the present it is and amaze around, explore and whatnot.