If you want to do a more professional install, you can buy a 746 series FAAC motor and controls for that type of gate, maybe $1000 total for new, or find one used. $300 and up.
http://www.faacgatesystems.com/proddetail.asp?prod=FAAC-746-CHAIN-PACKAGE-109775&cat=7
This supplier shows 230VAC only but they are available in 120VAC as well.
You can go rack and pinion or chain drive either works, chain drive is less work to set up.
Don't forget the safety devices, either safety beams or ground loops and watch out for pinch points if you have young kids.
I don't think the regular door operator would have enough power to run that gate as is, you would need to get it running without much rolling resistance otherwise it will bind and get stuck.
I own a company that installs gates as one of our services and we are asked to automate existing gates from time to time, so I have a bit of experience with this topic.
If you need any specific advice you're welcome to PM me.
BTW that Aleko brand looks OK, I do not know it personally but the pricing looks very attractive if it's well built.
Regards,
David