As Arch says it reacts against your foot. The front of the pedal pushes up a bit harder, and the back a bit less hard. The (geared down) motor reacts against this to apply a moment to the rotating crank, doing work on it and so helping propel the bike.
The work the rider puts in to their pedalling should be unchanged. Any extra work needed to oppose the front of the pedal pushing up is balanced by the reduction from the back of the pedal not pushing up so much. As it's activated in proportion to the pressure applied by your shoe to a pressure pad at the middle of the pedal, if the force at the back edge ever goes to zero (when your foot would lift off it) then the assist would cut out or reduce anyway - it's self limiting. The same system means if your foot slips off or whatever it will simply stop.
As the pressure between your foot and the pedal is distributed more towards the front of the pedal when it's adding power, you will presumably need to resist ankle movement with a bit more force via the Achilles tendon, as the pedal force has a slightly longer moment arm. But this is essentially a static force so will do no significant work. Opposing static forces does tire muscles, though, so I guess your calf muscles could tire a bit quicker with the pedals switched on. But I think it would be a fairly small effect, especially as you'll rarely be at full power.
The target for the production model is apparently 100W per pedal MAXIMUM assist.
To get 100W power at say 60 rpm, you'd need a torque of approx 16 Nm as per e.g.
here.
Assuming the pedal is say 6" long (15 cm = 0.15 m) then the difference in force between the front and rear ends of the pedal would need to be around 16 Nm / 0.15 m = 106 N. Expressed as kilograms of force that would be about 10 kg, so 5 kg extra push up on the front and 5 kg less push up at the back. I concede that is a 'best case' figure as the load would not be concentrated at the front/back edges. But + or - 5 kg seems reasonable given it's MAX power, when you're already fairly heaving at or standing on the pedals, applying presumably a decent portion of your body weight.
And remember the pressure sensor control system means it will only exert these forces when your foot is already stomping down with greater force. If your foot pressure reduces, so does the assist.
You'd want to use reasonably stiff-soled shoes I guess.
But there is no basic reason why this won't work.
Disclosure - the inventor Stephen Britt is a subscriber to Velo Vision, and I helped him distribute leaflets and show the prototype system to all comers at the recent York Cycle Show, as seen (fourth pic down) here:
http://www.velovision.com/cgi-bin/show_comments.pl?storynum=1114
I also sent out details of it to my media contacts which resulted in its appearance
on the Bicycle Design blog,
in Wired magazine,
on Engadget,
on road.cc,
on Tom's Guide and more. Any help I have given it has been free of charge and I have no stake in the invention. My motivation is to see £50k taken from Barclays bank and go to a cycling invention rather than to something less worthy, especially to a cycling invention which (like other electric bikes) has some potential to tempt people into cycling who might not otherwise give it a try.
Incidentally the inventor is IMO not daft, stupid, physics-challenged or a con-man. He seems like a very nice technically-minded chap with a good idea but whose strengths are not necessarily in explaining it or in marketing (Exhibit A being his 'promotional' video at the link below!). I think it's worth any help I can give it to get him the £50k to commercialise it (that's not even a lot of money for such a project).
If anyone else thinks it's worth a moment of your time to encourage go to:
https://www.takeonesmallstep.co.uk/Entry/View/2462
and give it your vote!