Well, I have absolutely no data to bear on whether or not gay guys tend to be more extreme in under/overachievement than our straight brethren are. So it's entirely possible there's no phenomenon to explain in the first place.
BUT, for the sake of argument, let's say there is a greater disparity. Some possible causes of this:
On the overachievement side:
1) As has already been mentioned, some gay men may build more of their self esteem off their schooling or jobs than is true of the average population. Consequently, those men are more likely to be considered overachievers.
2) Some of us gay guys were aware we were gay in high school, and not comfortable coming out yet and/or not in a location where there would be enough known gay guys for dating to be a major high school activity. Removing dating from the high school social calendar leaves a lot more time for school work and pursuing interests that employers and/or colleges would care about. It's also much less likely that we'll get a girl pregnant and have to come up with child support as teenagers. Being really busy is also a plausible reason for why we're not dating. The circle feeds on itself.
3) Outside of the rare school like BYU, academia is in general a very gay-friendly place. Domestic partnership benefits abound, sexual orientation and often even gender identity are included in the non-discrimination policies, etc. It is entirely possible that this leads gay men to, on average, stay in school for longer and earn more and higher-level degrees than straight men.
4) More gay men choose not to have children than straight men do. For those scoring overachievement primarily on the job scale, those guys will be more available to work longer hours, take extended business trips...and get promoted.
On the underachievement side:
1) There are still many families who withdraw essentially all support from their gay sons. A higher percentage of homeless teen boys are gay than is true of the general population, for example. Without family support, and with the military route closed off, these young men are in a much harder position when it comes to getting an education. However you choose to define underachievement, if a guy wants to be an architect, and would be good at being an architect, but never becomes one because he can't afford the degree and training, that's going to be a case of underachievement. Substitute any education-dependent profession you like.
2) Relatedly, some gay men are going to be in environments where they feel less than their straight counterparts merely because of their homosexuality. I admit that I'm thinking primarily of religious communities/families were homosexuality is viewed as a sin, but there are other possibilities as well. This can easily lead to depression, and with depression comes the serious possibility of alcohol and/or other drug problems.
3) Common perception of a gay lifestyle is fairly materialistic. The latest fashions, expensive food and wines, etc. all add up. Tickets to the symphony are probably more expensive than tickets to the monster truck rally. The chic gym with the juice bar is more expensive than playing basketball at the Y. A fine restaurant is more expensive than KFC, and Whole Foods is more expensive than Walmart. It is also generally seen to be rather youth-focused, with some seeing 30 as over the hill and 40 as in the grave (though there are plenty of men on this site who are clear counterexamples to those ways of thinking). It is entirely possible that a higher proportion of gay guys live well beyond their means trying to hold the lifestyle they think is expected of them, and this debt holds them back dearly later in life. This also ties in if you believe that working retail is a sign of underachievement. Anecdotally, I know a number of gay men who work in retail even though they have the education to have careers which both pay better and don't involve customers yelling at them all day specifically because of the employee discount on the clothes.
4) The arts are a realm that is incredibly welcoming to gay people. And some artists do earn huge amounts of money. Most, however, either barely scrape by or can't really live on the income as an artist, be it visual, performing, whatever. If you want to be an actor or a singer or a model, you probably need a day job with pretty flexible hours, and that's one of the main reasons artists often turn to food service. Food service is a hard profession to hold for an extended period--your income is subject to forces completely beyond your control, you get blamed for things which aren't your fault, and many people treat you as less than human during your job. If you wake up one day and decide that you're never going to make it as an actor/singer/whatever, and now you're 35 or 40 and all you've ever done is food service while trying really hard to get into another field...you'll probably be rather unfulfilled, and possibly end up with that depression issue already discussed.
As I said, I'm not even sure there's a real phenomenon to explain. But if there is, these all seem like plausible contributing factors.