Tetrominos fall down from the top one at a time. The object of the game is to stack the tetrominos without leaving any gaps.
Use the keyboard LEFT and RIGHT arrows to rotate the currently falling tetromino and use the DOWN arrow to make it fall faster (falling faster gives a bigger score). When a row is stacked neatly (that is to say, with no gaps) then the row is deleted and more space is available in the stack. Try to keep the stack neat because once the gaps get burried at the bottom the available space to maneuver gets rather tight.
The game ends when the stack goes right to the top of the hole.
Ownership of a trademark is pretty cut and dried, it restricts people or businesses from misleading consumers by placing the trademark on an item that is not approved by the trademark owner. The objective is to avoid confusion. So long as the consumer can clearly understand the difference between the genuine trademarked item and some other superficially similar item, then no violation has occurred.
An excellent example is Monster Cable, which is a hi-fi product and clearly unrelated to various other products that might also be called "Monster", and also quite distinct from the generic term "Cable" which might be any piece of multistranded copper covered by clear plastic insulation. You can read more about the discussion of trademarked products vs generic products, here.
Ownership of a vague concept (such as tetromino stacking), is a much muddier realm. Copyright law protects the expression of an idea (for example, computer source code is considered protected by copyright) but it does not protect the generic idea itself (reimplementation of the same idea in new and different source code is a distinct expression as far as copyright is concerned). Patent law covers material transformations and industrial processes, but no one has really managed to apply it to games (although the possibility exists that someone might in future patent a game, it is not possible to patent any ideas after they have been published and have become well known).
Just to make things crystal clear, the game displayed on this page is not Tetris, nor is it any product of The Tetris Company.