No, it can be used by someone without RMXP as long as you include within it all the resources you use. You see, RMXP works off of an RTP (Run-Time Package) and this folder is accessible by all projects you create. The problem, of course, is that this folder is located outside of each individual project, and so none of the resources you use from it are saved in the project itself. What this means is that if you give someone the game, and you used RTP resources, then those resources would not be included and thus would crash the game when you come across a situation where you need them.
You can fix this problem by making sure to include all of the resources you use in the project when you distribute your game. This is pretty easy, all you need to do is import the resources you use through the Resources Manager. Then, there will be no problem sharing your game.