If a client called me or sent me photos of this, I'd think "Hmmm, lessee here; he doesn't know for sure how to engineer this properly, and he's giving me the information over the phone that he thinks I need to do it right. That first fact, unfortunately, means he might not be telling me something crucial that he doesn't know he needs to tell me. If I respond with information tailored to what he's telling me and this is done wrong, it will become obvious that I should have come and investigated it myself."

I say either overbuild or hire an engineer. If you do it yourself, no matter what we say about it, you might think you're overbuilding but not be.

For instance, you have not mentioned whether the two displays will be next to one another but we can ASSume they are not and so must be designed as independent mounts and we could be wrong to assume that. You have not defined "fastened" or "anchor," and you have not given any indication of the strength of the wood structure or its resistance to sideways forces beyond telling us there's glass in it, which we can use to ASSume structural strength and wind resistance (thus resistance to the lateral forces involved in tying TVs to it).

I say either overbuild or hire an engineer. I prefer the latter. And that is a cost above and beyond your installation charge, which you should insist on for the safety of the client and the client's clients. Nobody wants a monitor spoiling their day by falling on their kid or in their spaghetti.