It's absolutely necessary; it should, in fact, be illegal to omit a volume control on any audio-playing control, embed, device, or otherwise. This is a bit of a tangent, but stay with me: Much like with playing audio without asking for an opt-in (PLAY button), not having a volume control makes assumptions:

a) The computer's volume is at a sane level.

b) The video or audio has a volume track recorded at some standard volume

c) by extension, ALL audio is always at the same level, and therefore a user would never have audio turned up to listen to some prior softer audio

d) The user doesn't already have some other audio playing, or that your embed audio takes precedence over that.

e) Their speakers have volume control; they might have headphones on. You don't know their sound situation, you can't make assumptions about it.

The reason I go so far as it being illegal to automatically play audio, and not offer even per-embed volume control is because this all has the potential to cause serious damage to their ears, equipment, and health.

That's why! :)

I agree, it's not necessary. However, I feel some users are accustomed to it being there, and so removing it may cause them a moment of confusion.

Maybe they want to have your volume turned down but still hear the "bing" over another event. Or any number of other scenarios.

Don't assume your video will be the only thing going on or the thing that determines the master volume setting.

Finally, if the user wants to adjust volume for your embedded object, why should they have to change the master volume, and then have to remember to change the master volume back, afterward?