First, gambling is not illegal - only illegal gambling is illegal.
Lotteries are legal in the United States when operated by or under licence from a state (44) or territory (3). That's legal gambling. It's illegal when operated by somebody else.
Clearly, Omaze isn't one of these; but they aren't running a lottery. They are running a sweepstakes. Not only ...
It's not obviously illegal.
A lottery has all three of these elements:
consideration - i.e. something of value the participant must give in exchange for the chance to win
Omaze doesn't require you to pay to participate. The rules say "You can always enter any campaign for free" and "You don’t have to make a donation to enter&...
By your definition, it’s gambling
chance: you said prizes are drawn at random
consideration (paying something to play): eyeballs on a screen is something of value
a prize: advertising is something of value being offered as a prize
Whether it’s illegal gambling depends on local law.