The Wikipedia definition of Alt-right is not so useful because it almost entirely the opinions of leftists. Likewise, for Alt-left. Sometimes Alt-right refers to a small group of obscure extremists, and sometimes it refers to all Trump supporters in the Republican Party. Here is Vox Day's definition.
The Republican Party is split between the Alt-Right and the cuckservatives, as illustrated by this Wash. Examiner op-ed. The author is upset that a liberal journalist found some racist comments on an email list, and he wants to join leftists in seeking purges of anyone who is even vaguely associated with anyone expressing a racist opinion.
The Alt-Right is disgusted by this attitude, because it inevitably censors good ideas and empowers the Left to control politics.
Right-wing sites are often hit by Hitler trolls who try to embarrass the site with pro-Hitler comments. They are just trolls, as Hitler is dead and has no supporters alive today. The cuckservatives panic and delete any comments that offend the Left. The Alt-Right is happy to offend the Left.
In fact, the Alt-Right sees offending the Left as a necessity. The Ctrl-Left is all about achieving groupthink by silencing alternative views. The Alt-Right has a long list of policy disagreements, and it cannot get started unless it can present facts and express opinions.
So it makes sense for the Alt-Right to offend the Ctrl-Left, and to test the boundaries of their censorship. The censorship must be broken to get an honest and productive discussion of policy alternatives.