In my experience, from what it says on the box (Blood and Gore, Intense Violence, Sexual Themes, Use of Alcohol), most of that deems true. There is most definitely Blood and Gore in this game, but I think there may be an option to turn it off, however don't hold me to that. There most surely is Intense Violence; dragons in the game eat people, burn them, you may have to kill people, etc in order to complete quests. I haven't really seen much on Sexual Themes, and it may be referring to marriage, which isn't a very big part in the game, and it's completely optional. Finally the use of alcohol. In the game you have the option to eat various foods and drink various drinks which may contain Alcohol. There is also a side quest, which is also a small, small part, and completely optional, to have a drinking contest.
Skyrim also has a community of mod makers. A lot of these mods are very useful and fun in the game, however there are some suggestive ones on there. If you do end up getting your son Skyrim, these mods are not something that should be used. In the end, Skyrim most surely holds true to it's M rating. However you can make it less violent than it's made out to be. Try and pick the less violent quests, don't go on rampages through towns, turn off the blood (If theres an option), and don't get the suggestive mods for it. Skyrim is an amazing game, the landscapes are beautiful, there is a variety of things to do, and lots of fun to be had. Overall what is in the game is present in a lot of PG-13 movies. If your son can handle these movies well, he will be able to handle Skyrim. I would suggest watching a few videos on Skyrim content, and of course if he watches Paul's Skyrim series, that is a great example of Paul not doing violent things to make the game a bit more appropriate.
There are also a few games that could take place of Skyrim. My suggestion I am about to put out may not be as good as Skyrim, however it still has the same qualities and can provide the same experience. This is the Elder Scrolls IV: Oblivion. this game came out a good number of years before Skyrim, so the graphics are not nearly as good. However, the sound is good, gameplay mechanics are smooth, and it is still as fun. It does have the same reasons for it being M, Blood and Gore, Language, Sexual Themes, Use of Alcohol, and Violence, however since it is older, it may be a good option to try before Skyrim.
It's the parents choice on what the child plays and is exposed to. My mom has not been strict at all, so I am open to these kinds of games, and me as myself pick the games I will like, and would be appropriate for me as a person. Even though I have been playing M since I was 10 or 11, I am not a violent person, I don't have any desire to commit the actions in the games in real life, and I feel like I am mature about this kind of stuff. I would never play GTA just because most of the game is killing people, stealing, robbery, and those kind of things, but however I play the games that are more than just committing crimes for enjoyment. It's your choice to judge whether your 13 year old is mature enough for it in the end.