Floor time is important in addition to lap time because that's where they can get some exercise (especially if he lives in a small cage) and blow of some of that excess energy, which is what he's trying to do when he runs laps in his current cage.
For one pig, a 2X3 C&C is enough space but that's the minimum. Store bought cages are notoriously too small and basically a glorified litter box. I mean think about it - he has to sleep, eat and pee in that same little area.
Yes, I would make sure you put down some tubes (elbow PVC pipes are good for this) for him to crawl through, maybe some TP tubes (with glue taken off, of course) for him to toss around. Maybe some new hideys to explore. In other words, give him something for mental stimulation as well as for exercise.
Lap time does make for a very safe, secure space for your pig. This might also be considered "bonding time". It's a time for your pig to start associating you with positive things so he won't be as nervous when you come around.