SPECULATION BASED ON OBSERVATIONS
Pietro Maximoff, in the canon Marvel Earth-616 continuity, was unable to "share" his speed with other beings or objects of a mechanical or computerized nature. One of his pet peeves in the Earth-616 continuity is the slowness of everything used by humans.
In Days of Future Past:
The scene in the movie where he plays ping-pong by himself is an excellent way to introduce his power in the physical world.
IF the movie has granted him a speed-sharing ability, this ability would explain why mechanical devices like his Walkman are able to play at a speed he could listen to in his accelerated rate.
However, while this would work for the Walkman it does not explain the accelerated computerized Pong game.
However, if he is the same as the canon Quicksilver:
- This means the Walkman had to be modified to play music at a faster rate of speed for him to be able to hear it while he utilized his powers. He may have also used the music as a timing mechanism to consider how long he had before he would need to be done.
UPDATE: A propmaster indicated Quicksilver's Walkman was a stolen prototype for a device originally patented as a stereo-belt created by Andreas Pavel--in 1972, a potentially real device that was never put into production. REF: Tested.com: X-men: A Tale of the Portable Tape
The original idea actually has a patent image and specifications. A prototype was created and that device is what Quicksilver is supposedly using in the movie. It would be capable of being sped up sufficiently for his needs (though I suspect tapes would enjoy a much shorter lifespan due to the speed increase.)
- The video game would have also had to be sped up for his enjoyment, but it would require someone with specialize skills to do this by altering the game's rate of delivery. This would be possible if someone with the proper skills reprograms the game. It is conceivable he could have learned to do it himself.
A PLOT INCONSISTENCY
- Since he was able to perform two dozen feats in the few seconds once he attacked the guards, and the music played (for the audience) at the normal rate, it is implied he heard the music at the same rate but accelerated for his enjoyment.
But that does not have to be the case. We are not sure what he is playing on his Walkman. I have also considered it may be nothing more than a means of focusing his attention to utilize his powers fully. It may not even be music at all.