You have to scrape the actual link to it (hard to say how to do it specifically without knowing which language you use). Use any arbitrary HTML parser.

Search for all class="odd deactivate". This entity has a key called "xeid" which is the "random" element in the address you are searching for.

e.g. <tr class="odd deactivate" xeid="YkASWIUq">

Alternatively you could scrape the link directly. Just search for all class="name table-participant"", the first child of it has a key "href" which is the specific link you search for. e.g. <a href="/soccer/italy/serie-a-2016-2017/torino-sassuolo-YkASWIUq/"><span class="bold">Torino</span> - Sassuolo</a>

I'm wondering if anyone has faced the same problem before? Thanks!

Yes, betexplorer does the same

Why would you enter the most highly competitive part of the affiliate market, which is already dominated by behemoths? What would be your USP in the niche?

Also, the bookmakers deliver the feeds to Oddsportal, oddschecker, betbrain and the like. They pay to be featured. You've got it the wrong way round.