You already answered your question.

"my PC is really old"

Quoting redviper37,

reply 2

Quoting ,

quoting post

I tried to play for first time and my PC is really old. But while playing, as the time passed, the game got laggy. And then even more laggy to the point I could not play. And then after I give up and close the game my PC was all laggy I could do NOTHING. Not even shutdown. I had to turn it off with the physical button.

Why is that? Could it be memory leak? Could someone help me

do you meet the minimum specs?  if your PC is really old, you may be limited to playing the smallest maps.

I did play in Tiny map size.

still, post your specs.  Or use Stardock support ticket to submit a report:
https://esupport.stardock.com/index.php?/Default/Tickets/Submit/Index

There's a general troubleshooting guide here:
https://esupport.stardock.com/index.php?/Knowledgebase/Article/View/496/135/general-galactic-civilizations-iii-troubleshooting

Lowering your preferences can help, if you have a really old pc.

You are square at the minimum configuration, maybe even below if your video card isn't 512mb.

The game could be laggy, but it shouldn't affect your PC once you quit the game.

In the troubleshooting guide above, try the part about reinstalling DirectX.

Also check the section:
III. Graphical issues

there's a file to download and copy in your game user directory, just follow the instructions.

I really think you should submit a support ticket with the link above and provide a full configuration info.
There is a tool to report hardware info I use, it's called HWinfo64:
https://www.hwinfo.com/download.php

Just run it, select "Report" from the menu and then "create".  Select the HTML option, upload the file to Stardock on their support site, along with your prefs.ini, debug.err and save game files (c:\Users\My games\Galciv3 (or GC3crusade if you have it).  They usually answer pretty quickly.

Maybe there's a leak that is only apparent on lower configs, it's a possibility.  Even on an older system, once you quit the game, it shouldn't affect Windows like that.

Also, make sure there is nothing else running at the same time as your game.

It's more likely to be an issue of memory management than memory leakage - with low system ram, Windows will be paging more and more things out to make room for the game's demands (which increase over time due to more things being present/getting calculated). Eventually it will get to the point that, even once the game has fully unloaded, the OS will stutter/stall for a long time afterward due to needing to effectively reload and reorganize everything.

A hard reset isn't a great idea if this is happening. Just let it sit (and undergo bouts of drive-thrashing) for a while and it should get back to normal eventually.