What are compound words called that are composed of words with similar meaning? Compared to classical Chinese, there are mostly words composed of more than one word/character. 
Especially the subgroup of VO-compoundwords (Verb Object) made from two characters have some special features, like the group of the lianheci. 

One subgroup are VV-compoundverbs composed of two characters with similar or near synonyme verbal meaning.

for instance: 磨 = rub, 蹭 = rub， 磨蹭 = rub.  


Is there a specific term for this group of compoundwords?
Do they have some special grammar rules unique to them?
You've asked an interesting question that the answer heavily depends on the example in your question.

When you see 磨蹭 as 'dillydally, stall', i.e. not a simple add-up of the characters, it is 联绵词 (binomes, see Baidu, Wikipedia). 联绵词 are words consist of two characters that are similar in pronunciation and/or meaning, but the meaning of the word is different from the individual characters (exceptions exist like 蝴蝶). You can find more information in the link. Some examples for verb binomes: 徘徊, 犹豫, 挣扎, etc. 

When you see 磨蹭 as 'to rub' i.e. rhetorical repetition, it is 同义复词 (synonym-compound, see Baidu). Note 复词 means 'phrase' instead of 'word', usually they are created on demand (although idiomatic 'set phrases' exist) and dictionary doesn't list them. This type of phrase has no grammatical significance over other types of phrase.