Sgt. Grumbles, a tabby cat, looks permanently grumpy but less so that Grumpy Cat. He has a strange habit of taking up a Pilates posture when his feet are tickled. The posture he takes up is designed to strengthen the core muscles (the abs and the lower back muscles). In Pilates the posture is not held but is transient.
Well, enough about Pilates (every Friday at 08:30!) – why is he doing this? Having considered it for a few minutes and scratched my head, it seems to me that he is stretching. He’s just stretching his legs. Cats stretch their legs quite a lot after they have been curled up resting. It is the preamble to getting moving again. It is the same for people. We yawn and stretch our arms and then reluctantly get out of bed.
The tickle on on his paws simply wakes him up or motivates him to prepare to get up and do something so he stretches his legs. It motivates him to do this because it is an interaction from his owner.