Learn Turkish: Bu bilgisayar sistemi hızlandırmaya yarıyor. - This computer serves to speed up the system.

The verb yaramak (to be useful for / to serve to) always requires its object to take the dative case (-a/-e). Standard infinitives ending in -mak cannot take case endings. To fix this, we use the short infinitive (or verbal noun) hızlandırma. Then we add the buffer consonant -y- and the dative suffix -a, essentially meaning 'for the speeding up'.

Since this lesson is about the -makla suffix, why aren't we using hızlandırmakla here?

Because the main verb controls the sentence! Yaramak strictly requires the dative case, so we must use hızlandırmaya. You use the instrumental converb -makla to mean 'by doing X'. To use it, you'd need a different main verb, such as: Bu bilgisayar, sistemi hızlandırmakla zaman kazandırıyor (This computer saves time by speeding up the system).

Could the phrase Bu bilgisayar sistemi translate to 'This computer system'?

Out of context, yes. Bilgisayar sistemi is a common noun compound for 'computer system'. However, context is key here. Bu bilgisayar is the subject ('This computer') and sistemi (with the definite accusative -i) is the specific object being sped up ('the system'). If 'This computer system' were the subject, the sentence wouldn't tell us what the system is trying to speed up!