These are not chip making machines. On a circuit board you have components and the PCB, with the PCB holding the components, furthermore the components can be IC's(chips) or passive components like resistors and capacitors. The machines you saw handle putting the components onto the PCB are used in the assembly stage of a product, with some of these machines being called pick and place machines.
Getting a career specifically as working with these assembly machines I do not know, but the field in general is known as EE, or electrical engineering. EE's deal with designing the products, from what components to use, how to use the components, and often times the people who are working in these types of lines are EE's. If you want to know about how to design chips themselves, you need a good bit of schooling just like an EE would.
Designing chips is known as what the other user said, micro/nano fabrication or IC design. You need to not only know EE (if you want to be able to design analog based IC's), you also need to get brushed up on basic chemistry, a good bit of high level math (calc 3, linear equations, differential algebra, etc), and of course some physics, all of which would be pointed out to you in schooling.
If you are interested, I recommend first learning some basic electronics (what is a capacitor, resistor, transistor) and then start getting familiar with micro-controllers, like an Arduino setup. Here is an example: https://www.sparkfun.com/products/11589
Once you are comfortable with dabbling in projects using microcontrollers and some analog stuff, you can look at FPGA's, which you can consider for now as a simulator of a chip. You write code using an HDL that describes a chip, and then that code gets compiled and sent to an FPGA which runs the code. Using an HDL like Verilog you can write your own processor without spending any significant money, and if you want you can actually get it fabricated at a company for a grand or two.
For an FPGA setup, here is a cheap yet capable for your purposes kit. http://www.terasic.com.tw/cgi-bin/page/archive.pl?Language=English&CategoryNo=139&No=593
You can find tons of really good books on amazon which may be outdated but still very valid for very cheap, here is an example: http://www.amazon.com/Verilog-Digital-Design-Frank-Vahid/dp/0470052627/ref=sr_1_2?ie=UTF8&qid=1373190276&sr=8-2&keywords=verilog
For questions and whatnot, make sure to check out http://electronics.stackexchange.com/
Buy this book. Helped my a ton while learning Verilog
http://www.amazon.com/Verilog-Digital-Design-Frank-Vahid/dp/0470052627