You can never be completely assured that whatever website you're connecting to is not serving you something malicious. However, there are multiple reasons why installation of malware on a specific user's machine would be difficult.
Typically speaking, whatever browser you use has its own security measures preventing the installation of malware. Code running in a properly working browser (theoretically) can do limited damage. (doubly so if you just do one thing on the browser, close it, and restart to do whatever you need to do next) If you're using an open source browser the likelihood of it being malicious is lower as you can just build from the source and everyone can see and audit the source if they so choose. If you're using a closed source browser, it's easier for a government to slip in malicious code by bribing the right people, but...
In addition to having to sneak in an exploit into a browser, they would also have to sneak in malicious code for a server to serve up. What a normal person views clearly isn't malicious (if it were, someone would likely notice quite quickly as well), so they'd have to serve up something specifically malicious for the target, which leaves room for discovery if a glitch occurs. Furthermore, exploits aren't laser-guided munitions. Once they're found out (and browsers are amongst the most actively probed software for vulnerabilities given their wide use by the public), anyone can exploit them and they will need to be patched out to protect the normal, innocent civilian (at which point your target has access to the security patch). This will harm the browser's reputation, leading to decreased usage and presumably decreased revenue. (much more so if it is found out to be intentional)
That said, if you upset a nation-state (or any exceptionally well-funded) actor enough, they can get around all that. Browsers aren't completely secure and you can buy existing zero-day exploits to bypass security measures, but they're a scarce resource and don't come cheap. (and you might need multiple to exploit someone) Bribing organisations also comes with a hefty price tag. At some point even if you really don't like someone, any benefit you might get outweighs the cost.
Instead, they may consider things like... just looking at the video being posted and attempting to figure out where it's being filmed (which if you believe 4chan, they've done and got the Russians to bomb an ISIS training camp, probably with something like a man-week of effort) or subpoenaing the website for IP access logs in case they aren't going through a VPN and then trying to use an exploit on other out-of-date software. Might even come with a free digital fingerprint even if you are accessing the site in a secure manner. Why spend hundreds of thousands of dollars or more if you can get the desired result for pennies on the dollar?
They could also just operate non-surreptitiously and force you to install spyware yourself. Or make you identify yourself to use most services. (to my understanding, this is fairly common in South Korea)
Or they could just bypass all that, and bribe one of your likely poorly-paid flunkies to give them the info they need. Or just indiscriminately drone strike places they think you might be since their citizens don't care too much about that sort of thing.
So really, the best defence is to not upset such organizations too much.