Could you explain this to a Brit? I'm interpreting your statement as when you register to vote that you have to indicate which party you prefer - is this really true?
If so, are you allowed to vote for the other party?
For example, the Democratic New York primary is a closed primary which means only voters registered as Democrats have the right to vote. However, the Democratic Californian primary is an open primary which allows voters registered as Democrats or as NPP to vote.
Voters can change their party preference at any time but they may be required to be registered under a specific party for a certain period of time in order to be given the right to vote in some States. For instance, in order to vote in New York you needed to be a registered Democrat for the past 6 months prior to the election date. This is a disadvantage to candidates who are well supported by independent voters (NPP) as many of them did not change their registration on time. That said, these rules are those of the party and while they can be considered unfair, this doesn't qualify for election fraud.
An election fraud tactic the report mentions is "registration tampering" which consists in switching the registration of voters without their consent and knowledge in order to suppress their right to vote. There have been numerous reports of registration tampering across most States with voters being switched from Democrats to Republicans or from Democrats to NPP and so on. Registrations seem to have been switch electronically (change in the database) some even involving forged signatures.
The confusing part is that the "Primary Elections" (which are held according to the rules of the party) are often run by the counties according to state rules, and are combined with other local elections that are open to all registered voters. Some parties in some states only allow those registered as belonging to their party to vote in their primary, while others allow "unaffiliated" voters to participate. The result is an mish-mash of private party rules and official state rules.
Party affiliation and primary elections have an odd semi-official status. Statistically, a little over 2/3 of the otherwise eligible voters are "registered to vote". Of these, about 1/3 are registered as belonging to the Democratic Party, about 1/3 are registered to the Republican Party, and about 1/3 are "unaffiliated". Something less than 5% of voters are registered with a "third party", and in recent history candidates from these parties haven't played much of a role except as a "spoiler".
Anyway, the current situation is that both Republican and Democratic parties have just officially chosen their candidates. The Republicans have allowed the public to "democratically" chose Donald Trump, much to the distress of many prominent members of the party who feel he does not espouse their values. The Democrat Party has chosen Hillary Clinton, but many (including many supporters of Bernie Sanders) feel she was actually selected by the party as their nominee well in advance, and that the "Primary Election" was being treated as a formality rather than a selection process.
The "General Election" for President happens this November 2016. All registered voters are allowed to vote for whomever they choose at this point. They can even write in candidates who do not appear on the ballot. But unless something unexpected happens to Clinton or Trump before then (or unless this is finally the year that a 3rd Party candidate breaks through) one of them will be elected to office at that point, and will begin serving in January 2017.
General elections are public elections in which anybody who meets certain requirements and is willing to invest the effort can run. As a public election any voter can vote for any candidate. If the candidate has been nominated by a political party, that party will be indicated on the ballot (and most Americans simply vote or the candidate nominated by their party of choice).
Primary elections are basically a private affair undertaken by a political party in order to choose a candidate who they will nominate for a general election. Primaries are facilitated by the public voting system and tend to be influenced by lots of state laws, but most of the specific rules governing a primary are left to the political party (and sometimes delegated to that party's state level organizations).
So parties get to make all kinds of rules about their primaries. In many states (it is subject to state law) parties limit participation in their primary to their members, or more often they disallow members of other parties (but allow someone who hasn't declared a party affiliation). The theory seems to be that this makes it more difficult for one party to ask their members to vote in another party's primary, in an attempt to nominate a candidate who wouldn't be viable in the general election.
All the adults in my family felt the fix was in for Clinton since 2008, as we assumed that she made a deal with the DNC regarding Obama's candidacy. If he lost, she would go ahead in 2012, and if he won, she'd go in 2016. So now it's 2016. I presume that the Clintons and the DNC have mutually-assured destruction levels of dirt on each other by now, so they must honor their deal. We never had any expectation whatsoever that any other candidate would get a fair shake. Nothing that has occurred since 2008 obviously contradicts the hypothesis. Secretary of state is #5 in the line of emergency presidential succession, and a perfect resume-builder for someone who didn't snag an elected office during the previous cycle.
We suspected that O'Malley was offered something in exchange for being Clinton's foil through primary season, and that he was able to bow out early, because former independent Sanders stepped in to fill his role as the token opposition, blissfully unaware as a party outsider that the fix was already in.
I am even now unconvinced that D. Trump was not a secret co-conspirator in the President Hillary Clinton plan. I'm not sure anyone expected the R party to actually select him, either.