Hi Tim,
Thanks for asking what is the most interesting question I have yet to see posted on the internet!
Of course my initial answer is "no idea", but there are ways... Despite the 1888 patent date suggested on the link you provided, the only Millet patent I can find in a quick search is Swiss patent CH9899 of 21 January 1895, granted to Felix-Theodore Millet for "Une bicyclette a roue automobile". The patent is very detailed, with 18 pages of text (in French) and 14 detailed drawings. Great stuff!
The motor is in fact fairly conventional - at least in the sense that it has poppet valves for the inlet and exhaust. The exhaust valves are driven by a fixed cam in the usual way. The exhaust pipes run down the spokes to a collector around the rear hub, thence forward to the carburettor amidships. Here the hot gases spiral around the carburettor to preheat the inlet gases and better vaporise the petrol, before exiting via the exhaust pipes labelled g and g' on your posted drawing.
The patent is a must read if you want more info. It is available online at the European Patent Office: on the advanced search page
http://ep.espacenet.com/advancedSearch?locale=en_EP just type 1895 in as the date and millet as the inventor and click "search". Let me know if you have a problem getting it and I will send you a copy.
Now my question for you: if you're not a vintage biker, why the interest in Millet's marvellous device?
Cheers
Leon