Is this a typical Chinese way of saying 'lack of strength'? Just checking: the following is not at all bad Chinese, or is it?

自主研发力量的薄弱，在某种程度上制约着民族游戏产业的发展。

I suppose I could also write:

薄弱的自主研发力量，

Either way I seem to have 'weak strength' or 'strength's weakness', which I suppose would need to be 'lack of strength' or some such.
Both expressions (the one you quoted and the one you wrote) are perfectly fine in Chinese.

薄弱 vs 'lack of' is a typical difference between language/culture mindsets. You can replace 薄弱 with 缺乏/缺失, which also sounds natural, but implies 'completely missing' to Chinese listeners. 薄弱 is the Chinese way to say 'somewhat/partially lack of'.