I think the simplest explanation is that it stems from the phrase “class act,” where class is an adjective. (I see LeoBloom has the same thoughts)

Also, I think maybe it works better than “classy,” which in a way, if you use that adjective to describe people, you probably aren’t. Futhermore, the word classy has become something of a joke and often has inherent sarcasm. If you call something really classy, you may very well be joking. It’s like calling a person “Slim,” which is basically the same thing as “Fatty” or “Fatso”—literal opposites, but the same meaning. (Or the opposite “fat chance” vs. “slim chance” both meaning slim chance.)

Can’t say that I’ve heard it a bunch, but I will keep my ears open for it.

I don’t know why “class guy” would be preferable to “classy guy”.

I looked on the OED and found that this usage has been around awhile though.

b. slang or colloq. Distinction, high quality; no class: of no worth; of low quality, inferior. Also attrib. or quasi-adj.
1874 HOTTEN Slang Dict., Class, the highest quality or combination of highest qualities among athletes. ‘He’s not class enough’, i.e., not good enough. ‘There’s a deal of class about him’, i.e., a deal of quality. 1884 Referee 24 Mar. 1/3 The elasticity necessary for anything like class at sprinting departs comparatively early. 1897 Daily Tel. June (Ware), Soldiers! Why, soldiers ain’t no class. 1924 H. DE SÉLINCOURT Cricket Match ii. 26 If he’d had coaching, he’d be a class bowler. 1927 [see ARROW v. 4]. 1927 R. REES Life’s what you make It xii. 161, I’m not ‘much class’. Ibid. 162, I am ‘no class’. 1948 C. DAY LEWIS Otterbury Incident ii. 18 Real class your sister is. Too good for a schoolteacher. 1954 ‘N. BLAKE’ Whisper in Gloom I. iii. 40 It was a class neighbourhood, thought Foxy, surveying the elegant, freshly-painted houses. 1969 A. HUNTER Gently Coloured iv. 52 I’m no class, I know that. I’m where I belong, a working policeman.

though you can see in these british examples that there’s a little different touch to it…

if someone on sports radio says someone is a class guy, they probably aren’t also saying that they think he’s from the upper classes (though in many cases it works out this way)

it may not have spread any further… thankfully

symbol of the oppressed masses Joakim Soria, try to support scores of impvoerished family members back in Mexico, actually turns out to be a dentist’s kid.

his sons saying that we were classy people

(1) In which sports are individuals most commonly described as “class guys”?

I would think baseball, although they seem to use it in college basketball a lot, especially when talking about coaches.

(2) Have you ever heard said use of “class” outside of a sports-related context?

Sometimes about actors and politicians (oxymoron?)

(3) Who invented the “class guy”?

What about Class Warfare my brothers? And I don’t mean the faux warfare perpetuated by the Foxnicks of the world, wherein the big bad media is supposedly drumming up resentment among the lazy and unionized agin the rugged individualist go getters with good old fashioned selfish values. I’m talking the real world, where the rich take from the poor, the dice are loaded, the good guys lost, Leonard Cohen, blah, blah, blah……class is used in horse racing a lot, if a horse drops from running against $10,000 claimers to $2,500 claimers, he is most definitely taking a drop in class.