In order to understand games you need to play and read games of course and preferably as many as possible. 

Game design is like any other skill: It needs to be honed and practiced and that can happen both by exercising it (make games) and by studying what the field looks like today and in the past.

I've talked a lot about writing games in the past and will continue doing so in the future, so let's talk about the second part:

Now, if you fancy yourself a designer you probably already buy a lot of game rules to read. However, if you are doing it to learn avoid the mistake of only reading games you are already interested in. Spread out and investigate genres, historical periods or concepts you would not normally play. Into hardcore fantasy simulation RPGs? Pick up a copy of Troubleshooters or Tails of Equestria. Platoon level WW2 gamer? Go have a look at what the Napoleonic guys are a doing and so forth. 

Heck read games from across formats altogether: Whether they are RPGs, miniatures games, card games or board games. Though this can of course be a bit expensive and I don't blame anyone for sticking to one thing. 

All game rules are basically answers to problems and you may be surprised at some of the problems you never even anticipated. You may also realize that many concepts are pretty universal: All miniatures games have some sort of movement system for example. 

It is also enlightening to study what problems a game does NOT solve or omits altogether. If a game does not include a points system, how do you set up a battle? If a game has no morale rules, how does that affect gameplay? 

Of course many subtleties are not evident just from a read-through of the game rules and you should endeavor to play new games as well. Obviously this is easier with games that you already have figures for. If you already play Chain of Command, picking up Rules of Engagement just requires figuring out the book, though more mercenary gamers may feel no reluctance in proxying figures for a test game.  You can even test the same scenario multiple times and see what comes out of it (as a friend on Discord did for science fiction rules). 

If you cannot find the time to do a full-blown battle of a game (especially some of the more involved ones) try setting up a simple fire fight or encounter. For example one unit occupies a hill and two units are just outside charge range and then simply play it out to see what happens. You can still gain a lot of insights from this sort of snapshot experience, even if it does not tell you the full picture of how every piece interacts.