I also have the same problem. I start game prototypes, often with only the art ideas in my head, and then try to figure out how to put it in a gameplay environment. It hasn't worked yet. mercuryus has the right idea. I have found that remaking other games in a simpler way is far easier than trying to make them yourself.
In regard to game ideas, all you need to remember is that the player must experience progress and challenge throughout the game. For example, progress expressed by having multiple levels or a score, and challenge expressed by platforming. That is the premise of the gameplay, which then needs to be backed up with gameplay objects; coins you pick up for score gives a sense of progress, spikes and enemies present challenge.
The trouble is thinking of those gameplay objects, especially without either referring to idealism like I do, or copying another game's entire gameplay structure.
Here are a few ideas.
Platformer based on randomly shifting level objects
The player has to get from point A to point B, and the level changes around them constantly (a seed based RNG could make this interesting!). Parts of the level would glow or fade as a warning, and then change randomly. Most of the time you would be unable to progress until this happens, meaning you would need to use strategy and reflexes to succeed. I was thinking about doing this myself, but it's a bit of work to make everything happen seamlessly. Anyone interested in doing it with me to make it more worth the while?
This one is hard. It involves only the elements of three different boxes. One is the player, one is the goal, and one is the enemy. The player can move a set number of spaces in any one direction, and the enemy can move any number of spaces in any one direction. It also teleports occasionally just to make it interesting. The idea is to get to the goal without being caught by the enemy, and since the enemy can only move in one direction at a time, it should be possible to do so, but require at least some strategy. The AI would be really hard if you wanted to make it super difficult.
The player is a gladiator in an arena and must fight waves of enemies to survive. They have RPG elements like inventory, skills, etc. or just score and a good weapon.
You are basically Liam Neeson. You go to places, people die. Progress is expressed by levels and score based on how quickly you complete levels, how many hits you take etc. and challenge is in level design and enemy placement. Basically you rush in, shoot people, and call it mission accomplished. Basic shooter.
I was considering making a topic for gameplay ideas and their gameplay objects, which people can attempt to create (and add to the OP) for practice/fun/etc. Would anyone be interested in doing this?