Where's the drop kick?
 

I was playing out a game and my team was down by 4 points. My defense recorded a safety later in the quarter, putting them down by 2 with 3 seconds left.

On the free kick we fair caught it at the opponent 45 yard line with just 3 seconds left. Isn't there a rule where my team can attempt a free drop kick field goal?

I don't see this option in the game...

It does NOT have to be a drop kick. However, a team does have the option to take a 'free' kick from the 45 yard line, sort of a kick off with no chance of it being blocked.

So, yes, a team should have the option to take a kick after a fair catch.

This option does not exist in college football for reasons I'll let folks google.

While, yes, you are correct as to the NFL rule, it is such an obscure rule with such a specific set of circumstances to its application that it is probably more of a pain to code in to the game than it would be worth to the actual game play experience. There hasn't been a successful free kick in the NFL since 1976. And prior to Phil Dawson's attempt in the NFL this year it had been 5 years since one was even tried. Personally, while I understand it is not 100% accurate, I'm OK with a once every 5 years-or-so event not being coded into the game play.

If you are talking about realism of the game experience, though, I'd be more concerned with an NFL punter/kicker booting a 25-yard non-onside kick into the field of play on a post-safety free kick, then the option to try a free kick after said shank.

(And as an aside I don't think any of the Xbox or PlayStation NFL games had the free kick coded into the game play, either)