I predict Kasich challenging Trump in the primaries, should Trump run again. In the event that Trump runs again but has not had a successful term, I think Kasich will stand a good chance of getting the Republican nomination.
Why Kasich? Primarily his outspoken opposition to Trump, and credentials within the mainstream Republican party, which will only be stronger if Trump does not succeed. And after 2016, he should have sufficient name recognition in 2020. Other candidates could challenge as well, but to me Kasich is the prototype of the prominent, fairly-well-known anti-Trump Republican with presidential ambitions and (unlike Trump) at least decent qualifications. I could see Paul Ryan, Ted Cruz, or Scott Walker considering a run as well, but I'm not sure if they're sufficiently anti-Trump either to run, or to win the primaries if they do. Particularly
Lyin' Ted, with his early support of Trump - if he tried to run, Trump would surely attack him on that again and it might help Trump again, too.
Democrats, I'm less sure. I don't think Clinton will run again, although if Trump is sufficiently bad she might actually have a chance. But the last thing the Democrats want is another William Jennings Bryan record of repeatedly being the nominee and losing. Biden has popularity, but is old, and Sanders' message could be be more popular yet, but again he's also old. Then again, if Trump is also running, that may not be too much of a liability. Who else has the name recognition? Most of the people being talked about, like Gabbard, I hardly know about at all. Harry Reid is retiring. California's best-known Democrats (Boxer and Pelosi) are likely either too liberal, or too establishment, or some combination of both. John Kerry already ran and lost, and is over 70 himself. Someone from Obama's cabinet perhaps? A representative who proves adept at either opposition to Trump or compromise with moderate Republicans to nullify Trump? I suspect we'll have a much better idea in a year or two.
And what about Michael Bloomberg? Either as an independent or a Democrat. He's considered it before, and while again he'd be fairly old, he wouldn't be much older than Trump, or older than Biden. If he was considering it in 2016, before deciding Clinton was good enough, I could certainly see him going for it in 2020 if Trump proves bad enough and there isn't a sure-fire Democrat to get behind.
So to sum your guys' position: The candidate you wanted didn't win, therefore democracy and rule of law MUST be dead in the US. Also, if Trump isn't immediately removed from office upon being sworn in, then it must also mean rule of law and democracy MUST be dead..
The problem is not the desired candidate not winning, it's that the winning candidate's respect for the democratic process is dubious at best. Between his professed admiration for multiple rulers who have, to be generous, been unkind to the democratic processes in their country, his hesitancy to say he would willingly concede the election during the debates is, as far as I'm aware, unprecedented. Combined with his narcissistic personality and thin skin, and if there's any "politician" that I wouldn't trust to behave properly upon losing, it's him. Cruz, Rick Perry, Rick Santorum, Sarah Palin, to name just a few of the more conservative Republican choices in recent years, while I would have had strong disagreements on policy, I would trust to not abuse the system of government when in power. Trump, I have essentially no trust, and it's only the pressure that would be exerted on him from the mainstream Republican Party and the leaders of the armed forces that make me think he would set aside power in 4 years should he run for re-election and lose.
And the real concern isn't the rule of law and democracy being dead now (although the civic health of a country that elects so unqualified a candidate should be seriously questioned), but what will happen to it while Trump is president, and should he lose in 4 years.