A Marine Rifleman is a jack of all trades. While our job is to focus on closing with and destroying the enemy, it doesn't stop us from learning the basics of other jobs. Some times, sure, it's to fill up training time slots but, why not learn how to use machine guns or mortars? Learning a little bit of everything is exactly why the infantry rifleman would fall under the class of "fighter" when it comes to table-top RPGs.
"Fighters learn the basics of all combat styles..." Is a sentence you'll find if you look at the Dungeons & Dragons Player's Handbook if you look under the class of "Fighter." The writers of the handbook may not have intended for this sentence to also describe the Marine Corps' main attack force but, it does a nice job of summing it up. But we're not going to stop there.
Here's why the infantry rifleman would be a fighter: