Speaker wire is low voltage. Yes, a meter would tell if they were actually hot, but it surely would say no here anyway. If you are truly paranoid, then feel free to put wire nuts on them, or even easier is electrical tape. It can't hurt.
In fact, I have some speaker wire hanging around myself, left by the previous owners of the house. It comes out of a corner near our staircase. Since I have absolute knowledge that it dues nothing, I've just left it there. One day when we redo the carpet in our house, it will get torn out.
HDMI and speaker wire are basically signal wires, not power wires. Both the voltage and amperage is very low. Indoors it is safe to run these hidden or exposed without channel or conduit if they are properly rated. See this Q&A for a discussion of proper rating.
When channel or conduit is used, it is either for convenience in handling, and to keep the wires away from other materials, or it is used to improve the aesthetics - channel can be painted and looks neater than cables.
There are limits as to how much signal wire can be run in cable or conduit, but this is generally a function of pure physical space and ability to pull wire, rather than heat or safety. Speaker wire can be tacked to baseboards or other molding if that works. be careful to avoid breaking the insulation or the inner wires when stapling, and if you put wire under moldings, be careful not to nail through. Its not a danger issue, is a broken wire/no signal issue.
Power, including extensions to run a projector, is very different. No code allows extension cords to be buried in wall. I don't think any codes allow extensions to be tacked to baseboards. Also power cables should not run parallel to signal wires - they can cause interference even though many signal wires (like HDMI) are shielded.
You need to bring a regular, properly installed power line to the projector. This can be properly installed NM cable inside a wall to an outlet box. It can be surface wiring, but this requires standard metalic surface channels and boxes such as this and this:
One other note. Lampcord is often used as speaker wire. It is the same as is used for AC power cords and small extension cords. If you are using such wire, be careful, if you are burying in walls or stapling, that it is speaker wire rather than power carrying wire.
Best Answer
It looks like the intent was to have your "media center" be placed on the far left wall. This is why you would have 4 electrical outlets and the coax connectors. This is the location you would either want to place your TV or projector screen. If you do go the projector route, placing the screen on the far left wall gives you the distance needed between the projector (placed near the outlet on the ceiling) and the actual screen.
The speaker wire does seem a bit odd. The way I would use it is to place 2 rear speakers in the top right and bottom right corner. These would be feed off of the lines that run toward the left of the room. Then your front left, center, and front right speakers can be easily run to the electronics on the left wall since they are so close.
You haven't specified, but if I designed a room in that fashion, I would have run 2 channel speaker wire (4 wires per jacket). This would then allow you to add the side speakers if you wanted to hook it up that way. Maybe the speaker wire you show has 4 wires in it to be used in this way.