At that age, if he is happy laying on his playmat or propped in a bouncy chair then watching you do chores IS an activity for your little one! Mind you, playing with him is bound to be more fun for you :wink:
I'd say find a balance that makes you happy, and your LO will enjoy having a more relaxed and happy Mum. If you are stressing about the mess or not getting to rest or do your own thing when he naps then play-time won't be so much fun for either of you.
As he gets older and more mobile you can give him chores of his own - plastic tubs to play with, pots to bang with a wooden spoon and eventually a brush to sweep the floor with or 'washing-up' bowl - while you get stuff done along-side.