MMA is unsurprisingly less dangerous than boxing concerning non-superficial injury (no gloves=less likelihood of hard hits to the head, since that will also often result in broken knuckles), “You’re more likely to get injured if you’re participating in mixed martial arts, but the injury severity is less overall than boxing. Most of the blood you see in mixed martial arts is from bloody noses or facial cuts; it doesn’t tend to be as severe but looks a lot worse than it actually is.” [1]
The science on football vs. MMA is murky, and I don't know if a definitive ranking can be established, but aparently it's more common to play through a mild concussive event in football, according to a current MMA fighter & former footbal player when asked which sport was more harmful: "It's football," Saint Preux said. "Obviously anytime you get knocked out, you get a concussion. You get hurt, your bell gets rung, that's a concussion. What usually happens is you play through it. Week 1, you get a minor concussion, you keep going. Week 5 comes around, it's worse." [2]
I would expect that overall the board sports are safer, but that when injuries do occur they tend to be more serious. For instance, I normally don't suffer any injury at all when skiing, and the worst injury I have ever received from skiing is a sprained ankle. However, I don't consider skiing a 'safe' activity, since the consequences of a mistake could easily be as serious as having an accident on my motorcycle, such as hitting a tree or other solid obstacle. But I don't routinely expect to be injured when I ski, while a fighter or football player can reasonably expect at least some injuries every time they play (and oftentimes even practice). I would actually expect that overall sports like non-US football and basketball would carry higher risk of injury than skiing/snowboarding. Skateboarding is interesting, I was friends w/ a group of fairly serious skaters, and aside from superficial injury (road rash, etc) it seemed paradoxically fairly safe (anecdotally, it seemed more common for someone to sprain an ankle playing pickup basketball) and hitting your head was an extremely rare event.
I can't find a link to the full study (this page is focused on the relative safety of shooting sports), but according to [3], the ranking on injuries/100 participants is:
Football > Ice Hockey > Soccer > Basketball > Baseball > Running/Jogging > Skateboarding > Gymnastics
Ice skating is fairly low (0.7/100), and skiing isn't listed, but I would expect it to be higher. Fighting also isn't listed, but I would think it would fall between hockey and soccer.
[1] https://www.fightersonlymag.com/features/boxing-vs-mma-safer...
[2] https://bleacherreport.com/articles/2830774-football-vs-mma-...
[3] http://www.familiesafield.org/pdf/Injury_page.pdf