I realize that you think you don't want a USB mic, but I'm going to recommend one anyway: The Blue Snowball. I use one frequently for my Skype calls, and it does a much better job of rejecting the fan noise of my MacBook Pro than the built-in mic.
Keep in mind that the audio ports on a PC are descendants of the original SoundBlaster card. One of the features that has persisted over the decades is low-voltage plug-in power. Rather than a mono signal or the balanced mono signal that you'd expect from pro-audio gear, the PC microphone port appears to be mono with an extra low-voltage power line. You can easily identify microphones intended for plug-in power by their 3.5mm TRS ("stereo") jacks. If you plug one of these microphones into your mac, you will get nothing. This is because the audio-in jack on your mac expects a line-level signal, which is what you would get from a CD player. Without plug-in power, the signal will be too weak for your mac to detect. The problem is that just about all the inexpensive microphones out there are intended for PCs and their plug-in power ports.
So you have two options. You could get a microphone pre-amp (expensive) or a small mixer with microphone pre-amps (possibly less expensive, but also lower quality than a standalone microphone pre) and a pro-audio mic (also expensive). Or you could get a high quality "podcasting" mic with a built-in pre-amp and USB interface.
The first conference mic that you linked to has a 3.5mm stereo plug and needs a "sound card with a mic-in socket." That sounds to me like the mic needs an audio interface with plug-in power. Even if it doesn't, it generates a mic-level signal (much lower voltage than line-level), so your mac won't hear anything
The Philips mic doesn't provide enough information to judge whether it will work in your situation.
Even if the two conference mics were likely to work with your mac, they probably wouldn't solve your problem. An omnidirectional mic will pick up sound from every direction. You complain about your mic picking up "robotic sounds." That could either be a consequence of a really bad audio interface or background noise from your computer or something else near your conference area. A more directional mic will allow you to adjust what is picked up by your mic by turning it.