I tend to get a few of these from time to time. Basically majority of these are just spam and their attempt to gain backlinks. The giveaway is the request for you not to change anything i.e. remove the backlinks. They will no doubt be using a automatic system to fire out the request to as many websites as possible in the hope a few will post it.
We are always after new good content but rest assured this will not be unique to you, so if they are successful the article will be duplicated many times elsewhere so will be of little value to you SEO wize.
The fact the post contains unrelated links would ring alarm bells to me. Put the request in the round filing cabinet (the trash)
You could however if you like the topic they have written use it as a idea for writing your own based on the same subject matter.