No, Mega Miner has nothing to do with Mega Man. Though I'm pretty sure that at one point or another X had a weapon that could mine through certain areas that would lead to further upgrades and grant him the ability to do a hadoken later on in the game... but that's off tangent and not part of this game.
Mega Miner is a simple game. You're in charge of an underground miner and have to tunnel through the deep unknown in search of precious metals, gems, and who knows what else. Shadow and Flame as they say, but there's no reason to believe that that'll be the case in this game.
Basically, being in charge of a mining drill, your task is to delve deep into the ground for precious resources. To do this though, you're going to need to properly equip your mining drill with different drill bits, proper cooling systems, strong armor, etc... To get the funds to properly equip your machine, you're going to need to dig for resources. At the beginning of the game, you're probably going to start out mining measly bits of coal or iron, as the heat will prevent you from going any further for the good stuff. Once you've amassed enough money though, it's a good idea to invest first in a colling system, as that will allow you to mine deeper for more expensive minerals. Sure, a better drill will allow you to drill faster and go through stone, but on the other hand, there's always dynamite for quickly clearing your path. Remember children, in this game, dynamite is your friend.
There's no real storyline or anything to the game, though there are a few goals that you can aim for. As most of the map is obscured (unless you use a sonar pulse which will reveal everything in the immediate area) there's a whole lot of exploring to do. Still, there aren't really any dangers like balrogs suddenly awakening from the deep or perhaps boring too deep into a column of adamantine alá Dwarf Fortress, but the game is interesting enough nonetheless.
The deeper you go, the farther you have to travel to get back to the surface. This is where teleporters come in handy. These will allow you to move directly between the last placed teleporter and the one on the surface, thus saving you quite a lot of time and fuel. My advice, grab more than one of these, as you might suddenly find yourself in a tight spot with your chasis melting around you and your fuel rapidly depleting. Deploying a teleporter will transport you immediately back to the surface where you can refuel and repair.
Besides the basic metals and gems, here are also various hidden goodies scattered throughout the underground. You might find lost treasures, alien devices, forgotten relics, etc... Though there's no active opposition in the game, the sheer fun of exploring and trying to find all of the hidden things is well worth giving this game a shot.