I deal with this one first:
one suggestion for app store: app store should show only those apps or games that are compatibile with my system.
Generally speaking, if it's in the MAS, your Mac can run it. Most applications do provide a terse summary of hardware requirements in their description, especially if special hardware is required to use the app. So check the descriptions.
Knowing this, you now have an answer to:
Specifically, I'd like to play
- Call of Duty 4
- Civilization V
Can I play these games in my 13" MacBook Pro?
Check the descriptions for these games in the MAS against your Mac's hardware spec. If they meet the requirements in the descriptions: you're good to go.
To get detailed information about your Mac's hardware click the Apple icon in the upper left corner of the menu bar and select
About The Mac. In the small window that shows up on your screen click the
More Info... button and you'll be given a detailed run down of all the hardware in your Mac.
Is there any other website where I can check game compatibility for my MacBook Pro?
You've already hit on one source: the App Store.
Another route is to use Steam. You can filter games to purchase based on OS and within in each there is a general description of what you need to play the game in terms of hardware.
Game manufacturers also list compatibility and hardware requirements on their websites for any given game. Though, looking at the Civilization V website, I suppose they don't keep this information up to date as games are ported.
And as the final, canonical source, you can always ask the manufacturer of the software.