No, according to Gigabyte, this board is DDR3 only.
The ASRock G31M-S uses DDR2-667 or DDR2-800 modules. it supports up to 8 GB of RAM using two 4 GB modules.
Although very expensive, 4 GB DDR2 and DDR3 RAM modules can be purchased from many online retailers.
As long as they're the same type (DDR2, DDR3). The speed of the RAM should either be the same or higher than your original since the computer matches all installed RAM to the lowest speed. e.g. my computer currently has a 2GB 800MHz DDR2 as well as a 1GB 667MHz DDR2. But the RAM is set to 667MHz and isn't utilising the full 800MHz on the 2GB.
The Compaq SR1940IL supports a maximum of 2 GB of RAM, using two 1 GB modules of DDR2-533 RAM.
The Gigabyte GA-EP45-UD3P motherboard supports a maximum of 16 GB of RAM, using four 4 GB modules of DDR2 RAM.
The Acer Aspire 3620 Notebook computer can use DDR2 PC2-4200 (DDR2-533) or DDR2 PC2-5300 (DDR2-667) which are 200-pin SODIMM modules. The Acer Aspire 3620 has two memory slots and each slot supports up to 1 Gigabyte of RAM for a total of 2 Gigabytes. This system uses unbuffered, Non-ECC, 1.8 Volt RAM.
The HP Pavilion tx1250ee supports a maximum of 2 GB of DDR2 RAM, each slot holding 1 GB.
Most DDR2 800, or better (e.g. DDR2 1066) should work, but to be sure that the RAM is compatible with the the motherboard, you can check the gigabyte webpage and download the PDF of compatible RAM-http://www.gigabyte.com.tw/Products/Motherboard/Products_Overview.aspx?ProductID=2314
The HP Compaq Presario CQ62-200 and CQ62-400 series of lap tops has the most RAM. These will support up to 8 Gigabytes of RAM. The difference is that the 200 series uses DDR2 memory and the 400 series uses DDR3 memory.
The ASUS M51A-F1 boasts a very impressive 2 gigabytes of DDR2 SDRAM.
The Dell Inspiron 1521 supports up to 4 GB of DDR2-667 RAM, using two 2 GB modules
The type of RAM your motherboard supports can only use that type and no other. If you have DDR2, you can not place a DDR or DDR3 module. If you mean can the game run the same on another system with different RAM, then quite possibly, but the speed of that memory may not be suitable for it.