Is it ethical to watch recreational videos or listen to music on a portable work computer bought from a research fund?
Unless explicitly stated in the rules that they should have told you when you got the computer, you can do whatever you want that doesn't damage the machine or compromises your work. Common sense applies:


Playing a CPU intensive game at the same time you are crunching some numbers you need soon will slow your computations, so it isn't good. Playing the same game while the CPU is doing nothing else, should be OK.
Storing music or films in the hard drive is fine, but if you are running out of space for your data, they should go away.
If the university is providing some backup service, make sure you are not bloating it with gigabytes of your personal stuff. A few megabytes of configuration files of your own programs and other small things shouldn't be an issue.


One can argue that just by using it you are wearing off the battery, and that is costing your university money; but on the other hand, a new battery costs around one salary day, and if that is what it takes to keep you happier and more productive (even a tiny bit) for years, I think it is well worth it.

If you were to need the help of IT support (in my university is as good as nonexistent anyway), they may delete your personal files and programs if they think they are related to the problem, as  Todd Wilcox pointed out in the comment. If they were less understanding, you may even be told off for installing software that they don't know (mind you, it may even be research related!).