This is probably the best example of how different materials, despite appearing like you can machine them to look the same, will behave very differently. Wood is, in particular, very different from plastic and metal, because it is far more anisotropic due to its grain structure. Those long and narrow bosses are acceptable in a metal or plastic part, but won't hold up at all in wood. For a better solution, I recommend not trying to follow the exact shape as the plastic part for the internals, but have as much material as possible; if you need to, use longer screws.
Many electronics were housed in wooden cabinets for over a century (e.g. radios, televisions, turntables, etc.), so it would be wise to look at those for examples of how they used wood in their design.