Yes, you can re-install Google Play Store. There is a thread on the XDA Forums which explains how the procedure is done. There is also an APK file to install it on your tablet. Basically, that's all you have to do: download the APK, transfer the file, Check Unknown Sources in Settings > Security, then use File Manager to locate the APK. Tap on it and install it.
XDA thread: http://forum.xda-developers.com/showthread.php?t=1996995