I am fairly confident it's standard German. I can understand him rather well - I believe he says: "Ich bin Ludwig von Bayern, König dieser Lande. Der Schwanenritters alte Sage lebt in mir erneut."
I'd translate that as "I am Ludwig of Bavaria, king of these lands. The old legend of the Swan Knight lives in me anew." The official translation is close enough to that.
Whether he speaks with a Bavarian accent or not though, that I can't tell - I am not a native speaker to have ear for such nuances.
Im native german, so I can help out a bit. The only thing you have incorrect is "Der Schwanenritters", I think he says "Des Schwanenritters" which makes a lot more sense grammatically, though im not 100% sure, its kinda tough to understand and maybe it was correct 200 years ago? But to todays standard, I would say it that way. Your translation is spot on, nothing to add there, and Im not a complete dialect expert, but to me it sounds like a bavarian trying to speak "normal" german, because everything sounds "normal" except the word "Sage" (meaning something like Saga / Legend) which is pronounced a bit different. About the difference between what is spoken and what the subtitles say: In the end, they have the same meaning, but the word "embodiment" ("Verkörperung") doesnt exist in the voice lines, though it would work well and give it a nice, epic-sounding tone to say that you embody something rather than saying that something lives in you. Another difference is that the voice lines are split into 2 sentences and the on screen translation fused them together, which works well with the addition of "embodiment", because he says "I am [...] King of ... and embodiment of..." .
Here are some comments about this video:
-His voice acting is SUPER exaggerated, I dont know if there is something about Ludwig that I dont know, but for me it is far from a way somebody would naturally speak (bavarians could be seen as """weird""" speakers maybe, but what Im talking about isnt related to the dialect) and I actually laughed the first time I heared it because its lowkey funny (its a bit difficult to explain what i mean by "exaggerated", but it sounds like he is stuck in a movie and thinks he is the main character in everything there is, maybe intentionally to (strongly) portray a self loving character? Maybe some history experts can pick up on that one)
-> This also makes it tough to differentiate between exaggerated voice acting and a dialect, "Lande" and "alte", simmilar to "Sage", (maybe?) have a slight bavarian tone to it, there might be even more indicators for any form of a dialect, but since im not bavarian or a dialect expert and its difficult to tell apart, I cant help out more on that one
-I would phrase the last thing he says a bit different, he says "Des Schwanenritters alte Sage lebt in mir erneut", but I would put "erneut" before "in mir", both are perfectly fine, neither are wrong, I dont know if on microscopic level what he says is right / better, but in every day talk I would say it the other way around, specially when you want to sound epic, you make a cool statement, talk about how cool you are, and then "anew" is your last word, kinda weird isnt it, "in me" would be an """impressive""" way to end your sentence [Paying closer attention to this makes me think that why does something live in you "anew"? Wouldnt that imply that it lived in you before, died inside you, and now lives in you "again"? Or am I just interpreting that wrong?]
-Some germans pronounce "g" like a "ch" (not like "k" or "tsh" but a sound somewhat close to a "sh", I cant find an english word that contains that sound right now, the very first words he says ["ich"] has that sound), so "Könich" and "Ludwich" (still written as "König" and "Ludwig", just pronounced differently), but this voice actor doesnt, which I believe aligns with a bavarian trying to speak high german style of speaking (I think neither bavarian or high german exchange the "g" for "ch" [maybe im completely wrong and this "g" and "ch" stuff isnt related to dialects but to something else])
-This dude seem to like swans quite much, there are enough sources in english (even for the legend of the swan knight), maybe my history knowledge is bad or this whole swan stuff isnt really that big of a deal, he is in direct connection to the "Schloss Neuschwanstein" ("Castle Newswanstone" for those who want a literal translation on that), famous historic building, which is depicted in the background (and apprently in the background of Frederick as well), and he seems to have built quite a lot of castles ("a lot" needing a relation, anything over 1 castle built would be a lot for me, my quick research told me he was involved in building / planning / demanding / commanding / whatever word fits of at least 3 (bigger / well known / ...) castles, but he apparently built / planned / ... more, earning him the title of "Märchenkönig" ["Fairy tale-King"), and many times, the first thing you read about him is that he built castles, might be a hint to his leader ability, but, among other artists / cultural projects, he seems to have funded famous musician Richard Wagner, so being known for building castles and funding artists sounds like a cultural victory type of leader?
Maybe I will come back when the full voice lines are published and nobody else has translated that, and one last note: The difference between the literal translation of what was being said and the on screen translation is a thing I have realized when trying to translate german, many times I will translate a sentence, look at it and try to give a better / epic / cooler sounding tone to it, not refering to translating word for word and making grammar work, but having a fully functional english sentence and tuning it a bit without changing the meaning.
[If I am wrong on anything or missed out on key parts, feel free to correct me, I dont know a lot about Ludwig (in fact, everything I wrote about him is a result of a quick research) and though I am interested in languages I am not a professional]
It is interesting, though, that this person thinks that languages did not exist until they were written...or that languages cannot be written in multiple scripts (e.g., hanja is Korean written in Chinese characters, not Chinese)...or that Koreans appeared out of the aether when Sejong commissioned hangul. Does someone want to tell them that hangul was suppressed until the late 19th century for fear of the repercussions if peasants learned to read? 
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