Question: Let's consider a player, whom we shall call Bob. Bob loves exciting gunfights and is a big John Woo fan. So he makes up "Shooty McShootenstein," who is a master with a gun. One thing that Bob is *not* interested in is the cyberpunk hacking trope. So Shooty doesn't really have any ability at that. From the player's choices, it seems they want a game with lots of gunplay but no hacking. But here's what happens in practice:

* When Shooty gets into a gunfight, his high skill means he blows everyone away in a round or two, or a few minutes of table time. Bob's real choices during this time are largely restricted to taking actions to stack additional bonuses that are mostly unnecessary or making tactical choices that are often rote. Bob is left unsatisfied.
* When Shooty finds he needs to hack a computer, suddenly his choices open up! He can hire a hacker, threaten the owner, bluff about already having the information, etc. This will take considerably more table time. The problem is that it's still indirectly all about hacking and is exactly what Bob didn't want to play. He ends up bored because he doesn't like this theme and his character is bad at it.

Many proposed suggestions don't seem to help. Putting Shooty against better gunfighters is a good idea, except that in most systems, a gunfight between two characters with Firearms and Dodge skills at 20 have the same actions, probabilities, and modifier stacks as one between two sides with Firearms and Dodge at 2. Essentially, Bob might as well have played a much weaker character. Making the consequences for failing at the hacking-related stuff easier on the character might encourage Bob to experiment a bit, but fundamentally he's still going to be bored because his share of spotlight time was spent in 2 minutes about him being awesome with a gun and 2 hours about him being a lousy hacker.

What techniques can be used to overcome this contradictory tendency in play, either as a game-master or as a player?

Answer: 
This exact setup happens all the time in movies, so let's examine how they handle it.

If they are the only character, then as a GM, completely tune the story to them. They shouldn't have to do hacking, or at best they have to shoot their way in to where the Russian hacker who already knows stuff is. James Bond doesn't use keyboards. Avoid his minimums except for once in a while for dramatic effect, or to introduce Bond Girls who have that skill set. As for addressing his strength - he's an expert shooter, but is always having to go places where he doesn't have a gun, or just has a pistol when others have machine guns, or has a machine gun when they have tanks. Or places where you can't just shoot the heck out of everyone (like a public casino) without having long term consequences.

If they are not the only character, the other characters are in danger. What do The Killer and Hard Boiled have in common? Lots of OTHER people who get killed. The chick who's along that's in danger. Or your buddy movies with one killer type and one intellectual (or even just not a killer, take Rush Hour) - the killer has to spend a lot of their time protecting/coaching/handling the less combat oriented person. One of the big risks of having a min-maxed PC in the group is the min-maxed bad guys the GM has to toss on, who can often terminate the non min-maxed PCs in a round. It becomes the combat monster PC's job to avoid that, or else the whole party dies and they say "new game, and be less of a goon this time please."

This is of course advice for in-play. You should try to head this off ahead of time by disallowing (GM)/forgoing (player) total min-maxing by choice of system or GM guidance. Because as you note it ends up being unsatisfying even in your maxed area.
Provide Shooty with situations where he gets to use his shooting, but it isn't enough to just shoot. A gunfight doesn't just have to be some people shooting at each other.

Letting the NPCs have a huge situational advantage, and using non-standard dirty tricks is a good way to introduce tension to gunfights that have gone stale. For a prime example, check out [Tucker's Kobolds](https://media.wizards.com/2014/downloads/dnd/TuckersKobolds.pdf).