I'm pretty sure that if you will hold down the front of the case and then push back on the arm of the machine that it will probably snap out. I think some of the Kenmore machines may have had those kind of cases. It may take a bit of effort, but shouldn't be much. Remember you are tilting the machine not lifting it out. From the picture of the whole machine, it kind of looks like it wider in the middle than at the ends of the case, probably for a little more room to hold onto when tilting it back. Remember to have something to hold up the machine when it is tilted back.
It also looks like there is a hole in the corner, possibly for a lever to twist.
Janey - Neat people never make the exciting discoveries I do.