Learn English – What does the phrase, “ninesigma worthy,” mean

Ordinarily a fine point means a subtle distinction (sense 8a in TheFreeDictionary).

The fine point isn't a standard term in any context, but per @Robusto's comment, there is the fine (or small) print meaning (usually unfavourable) details buried inconspicuously in small print at the end of a verbose contract. In common parlance it's often assumed that such apparently minor details may in fact be of crucial importance when deciding whether to sign a contract.

In fact OP has mistranscribed "The fine points" (at 1m 45s) in an instructional video. As @Spare Oom indicates, a fine point is a subtle or abstruse point. Used in the singular that would often imply an obscure, peripheral detail, but in this particular context the speaker is using the plural, and his meaning is...

The subtle details which must be mastered in order to swim really well.

This doesn't seem like a particularly common usage to me, possibly because of the unwanted negative associations with fine print, and a fine point in an argument, which is often said dismissively of some valid but peripheral assertion. In OP's context there are no such connotations or other ambiguities, but I wouldn't advise using the expression more generally unless your context is equally clear.

Tutto fumo niente arrosto would easily translate in the United States to All hat and no cattle, which makes reference to a wannabe cowboy (or rancher) who dresses the part but lacks any real personal experience. It means full of big talk but lacking action, power, or substance; pretentious.

This link has a way of describing the expression as being rather derogatory, but has that U.S. Southern sound of politeness (in the same way that "bless your heart" is used) where one might get away with saying it to a person's face without them realizing how badly they have been stung. You can read the coarse language interpretation yourself at the link, but the oafish target might simply respond "Uh, thanks, so you like my hat?"

Country singer Trace Adkins has a song based on the expression. The lyrics might metaphorically describe your host fairly well:

See that boy standing there by the dance floor 
He's lookin' like the Marlboro Man 
Starched shirt, starched jeans, big trophy buckle 
And an empty Copenhagen can 
He's talkin' cowboy this and cowboy that 
Well I'll bet one thing's for sure 
The only stampede that he's ever seen 
Is the clearance at the western store

All hat and no cattle, that boy just ain't real 
All boots and no saddle, don't know how to make a cowgirl feel 
Think I'm gonna tell him to pack up his act 
And go back where he came from 
'Cause all hat and no cattle ain't gonna get it done

He's just a smooth-talkin', long-tall slow-walkin' 
Drugstore-made-up dude 
So honey don't you fall for that fake Texas drawl 
He ain't right for you 
What you need's a man that ain't just a hat stand 
When you get him home 
Well, I don't look like much, but I can sure saddle up 
And ride with you all night long

All hat and no cattle, that boy just ain't real 
All boots and no saddle, don't know how to make a cowgirl feel 
Think I'm gonna tell him to pack up his act 
And go back where he came from 
'Cause all hat and no cattle ain't gonna get it done

All hat and no cattle ain't gonna get it done

(You can hear the song at this link.)

From a description of cowboy culture in wikipeidia:

Actual cowboys have derisive expressions for individuals who adopt cowboy mannerisms as a fashion pose without any actual understanding of the culture. For example, a "drugstore cowboy" means someone who wears the clothing but does not actually sit upon anything but the stool of the drugstore soda fountain—or, in modern times, a bar stool. Similarly, the phrase "all hat and no cattle" is used to describe someone (usually male) who boasts about himself, far in excess of any actual accomplishments. The word "dude" (or the now-archaic term "greenhorn") indicates an individual unfamiliar with cowboy culture, especially one who is trying to pretend otherwise.

You should know that modern Texans (and Western Americans in general to a lesser degree), take the cowboy culture seriously. - I would imagine that the wealthiest oil barons, ranchers, sport team owners, and techno-wizards of the region would treat the cowboy culture just as the British Royals treat their foxhunting and equestrian sports. The phrase "all hat and no cattle" would be an often used phrase among these elite. (If you have ever acquainted yourself with the television series "Dallas", you may understand this better.)

By the way, let me point out the word wannabe that I used in the description above. (Wannabe cowboy, meaning someone who wants to be a cowboy or rancher). "Wannabe" is a derogatory noun, one who aspires, often vainly, to emulate another's success or attain eminence in some area.

Stuffed shirt (n) a pompous, self-satisfied, and inflexible person.

Pretentious (adj) characterized by assumption of dignity or importance, especially when exaggerated or undeserved; making an exaggerated outward show; ostentatious.

Pompous (adj) characterized by an ostentatious display of dignity or importance

Prideful (adj) having a high or inordinate opinion of one's own dignity, importance, merit, or superiority, whether as cherished in the mind or as displayed in bearing, conduct, etc.

Supercilious (adj) displaying arrogant pride, scorn, or indifference; feeling or showing haughty disdain.

Vainglorious - characterized by or exhibiting excessive vanity; boastful.

Slurring his speech while drinking at dinner makes me think of bumptious - (adj) presumptuously, obtusely, and often noisily self-assertive; full of ones self.

Of course, adding "jerk" or, better yet, "ass" to any of these adjectives makes them more disdainful, as with pretentious jerk or pompous ass.