There's no requirement for the VWP as to which country you are entering from.
However, there can be issues when leaving the US, depending on what country he's returning to.
When departing the US, he will need to show the airline his passport. There's two purposes for this - firstly it's so that the airline can confirm that he has a visa/citizenship/etc for the country he's traveling to, and secondly it's so that they can record the relevant information and pass it onto USCIS (US Immigration) to report that he has left the US.
The problem comes about if he uses one passport to enter the US (in this case, his Germany passport), but tries to use a different passport for the return trip (ie, if he has to use his Polish passport for the return due to visa/etc requirements). If he simply uses the different passport, then USCIS will likely not record that he has left the country, and this can cause issues if/when he tries to revisit the US as they will suspect he overstayed on his previous visit.
There's a few ways around this. The obvious one is to use the same passport when entering the US as when leaving. This is only a valid solution if his German passport is valid for entering his next destination (which is not to say that he has to use his German passport to enter the next country! It's just so that the airline can confirm that he has the required documents).
If that's not possible, then he should discuss the issue with the airline on departure. They are able to record details of both passports - one for US status, and the other for the destination country documentation check - but they likely will NOT do this unless he makes it clear to them which passport he entered the US on.
Previous this issue didn't exist as even VWP visitors had to fill in a form on arrival (I-94W) and on departure the airline collected this form as proof that you had departed, however I-94W forms have not been used for a few years so there is no physical tracking of entry/exit, only the tracking that happens in the various linked computer systems.