So, basically, the reflective form (s'agripper) is used when you need to say "to cling on to". It can be a person, a branch, life, etc. It can mean that you are hanging on something. The simple form (agripper) really means "to grip". So it's a way to say that you need to "catch" something, like someone's arm. This expression can usually be replaced by "attraper" which is more general IMHO. In fact, you could say, "je m'agrippe au bord de la table de ping pong", it would still work, but that changes the sense of the sentence. In your example it just means that you are grabbing the edge of the table, meanwhile in my example, it could mean that you are falling and are holding to the edge of the table to prevent it. See the difference between holding the table and hanging on to the table (kind of)? In conclusion, what حسن said sounds correct to me :)

aggriper is to grasp, to grip, to hang onto something; howerver s'aggriper means is to grab hold of something. for example when we climb a tree we can say "il s'aggripe a une branche"; in the other side aggriper is like to grab something or someone firmly, no need to clim anything hehe I hope I helped.

The simple verb means as the dictionaries state while the reflexive one might have more phrasal meaning, e.g. catches/seizes my attention (as in the first sentence you've provided).