I'm not a primal fitness expert (I mostly just walk a lot and make a conscious effort to use my muscles to lift moderately heavy things) so I'll let others comment on that part.
But I did wonder about whether you're missing the intent of the "play" part of primal. I don't think counting yet more exercise as play is quite the point...I think it's more of a "let loose, be a kid" kinda play. Sure, it could involve exercise (and probably will) but I wonder if weight lifting is the kind of exhilarating fun Mark meant? I think he intends real laugh-out-loud play so that we can forget our demanding office jobs and exercise programs and food issues.
Zone diet on and off for several years....worked, but too much focus on exact meal composition
Primal since July 2010...skinniest I've ever been and the least stressed about food