In any casino or online gambling site like Satoshidice with non-zero house edge players will always lose playing long term, but in the truely zero-sum game (i.e. where no house edge or any other commission fees applied) players will NOT lose anything playing infinite long.
This section may need to be reworded. Unless your bankroll is infinite, you will eventually go bust if you play infinitely long. Even though the expectation value of each bet is 0, play long enough and you will eventually encounter a losing streak long enough to deplete your bankroll.
Nah, that's worded perfectly.
By playing infinitely (Which it's stating), one also assumes infinite access to money. With that they will, in the long run, always end up at square 1.