Well, they're right -- a well balanced exercise plan does feature more variety. That said, I'm a HUGE proponent of calisthenic-type workouts, and I think that something like this is definitely more good than bad.
If you wanted to supplement this, without significantly increasing the difficulty, do something similar with situps on the off-days. If you're doing M-W-F for pushups, then do the same incremental workout with situps on T-Th-S.
Better still would be to add some walking to the mix. Walk a mile on Sunday, perhaps.
One other thing that I do to round out cardio (as I am also in horrible shape at the moment) is to start off each 'workout' session with jumping jacks. They're simple, easy, hard to screw up more than a little bit, and do a great job at getting you warmed up. Start with 10 or 20, and again, just keep incrementing upwards as they get easier. I personally would do jumping jacks (or jumping rope as they get easier) before every workout.
Regardless, good luck on your goal. Doing SOMETHING towards achievement is definitely better than doing nothing, regardless of how unimpressed your trainer friend might be.