There are multiple reasons to have unmovable files.
In a FAT drive you can set attributes for each file. These attributes are: (R)ead only, (A)rchive, (S)ystem, and (H)idden. Any file that is marked as read only, system, or hidden will be considered "unmovable". The reasons are obvious for the read only files - defragging them would violate the read only request. The reasons are also obvious for the system files - you don't want to screw around with an important file that the system might be accessing at the same time. The reason to make hidden files is outdated. Many older programs had copy-protection that made a hidden file at a certain location on your drive. If you don't know about hidden files, you didn't copy the file and the copy wouldn't work. If you were smarter and knew how to copy a hidden file - you likely didn't copy the file to the correct location on the new disk - and the copy again didn't work. If a defrag program moved the hidden file, then your program will fail to run so it became necessary to make hidden files "unmovable". As far as I know, no current program uses hidden files at a defined location as a copyright anymore. Thus it isn't needed - but must still be included in case you happen to have an old program with that type of copy protection.
In addition a file on a bad drive sector is also "unmovable" in many cases since the file cannot be properly read.
On a NTFS disk, you have more options. Files can be marked as "unmovable" since it might be protected, you might not have permission to access the file, or the OS might mark it as a necessary file in use. An NTFS disk also has all the file attributes listed above.
A pagefile is usually a hidden system file that is marked as in use - thus it usually is "unmovable". Sure you can safely move it - as long as it isn't accesed during the defrag of that file. On your laptop, this is most likely your large "unmovable" line.
Conclusion: if you want to move those files with a normal defrag you need to remove the read only, hidden, or system attributes and give yourself permission to access the files. If something goes bad, you are screwed and it is your fault. Or you can just leave them there since it doesn't harm you.