Does the value of Football Manager 2014 (gift) remains the same as time goes by?

Nope, you ain't. It's just that there are so many of these, and mostly people won't answer you properly.
Your best bet is to search on steamgifts.com/trades for how much people are selling the game.

Well you have to take two things into account:

• People who collect
• People who play

For the people who just want to collect, the value will increase I guess, as it is no longer in the store and it will be increasingly more difficult to get the game.
For the people who want to play though, the value is going to decrease, since they'll have new instalments of the series.

I'd try to trade sooner than later, collectors are usually very good at getting what they want, so it'll be harder to find some to trade later on.

In theory the value of games increases the longer they have been out of the store and they get rarer. But it only works in practice if you have a buyer.

Football Manager gets replaced every year. Anyone who wanted it knew to buy it in advance and plenty of traders stocked up in the final sale believing that it would be 'collectible'. But it isn't like games that suddenly vanish from the store and become collectible and it isn't ever going to be that rare. And anyone who just wants to play it will buy FM2015, FM2016, etc.

I suspect if you try and be greedy you will just end up stuck with the things.