If I can't win, but can stop my opponent from winning, is the game drawn?
No. If you in a situation like that in paper magic, you'll have to create a shortcut per CR:


  720.1b Occasionally the game gets into a state in which a set of actions could be repeated indefinitely (thus creating a "loop"). In that case, the shortcut rules can be used to determine how many times those actions are repeated without having to actually perform them, and how the loop is broken.


Also per MTR 4.4, you can't ‘opt-out’ of shortcutting a loop:


  A player may not ‘opt-out’ of shortcutting a loop, nor may they make irrelevant changes between iterations in an attempt to make it appear as though there is no loop. Once a loop has been shortcut, it may not be restarted until the game has changed in a relevant way.


The game could be drawn if both players were involved in a loop both would choose to continue indefinitely, but this is not the case:


  If two or more players are involved in maintaining a loop across turns, each player chooses a number of iterations to perform, or announces their intent to continue indefinitely. If all players choose to continue indefinitely, the game is a draw.