Well, that IS confusing. However, on the
same Inyo NF page you cited, it also says this:
On February 15th the applications that have been accepted to date, will be thoroughly stirred to assure random order and processing will begin.
The sentence you quoted (from the "When can I apply to the lottery?" paragraph) is about 7 paragraphs below the "What is the lottery process?" paragraph.
What they really mean is:
There is no advantage given to the first applications to arrive
between February 1 and February 14.
On February 15, processing begins, so some applications will be pulled on the 15th, some on the 16th, etc. So you miss the chance of yours being processed those days if your application arrives later. However, whenever your application arrives, between the 15th and 29th, it has the same chance as all the other applications that are unprocessed up to that point in time.
Processing continues until all slots are reserved, and the process is not completed until around the first of April. However, the most popular slots fill up early, so the later your application is processed, the lower your chances of being successful.