Yes he did. However, before signing the extension, he won the Hart trophy. He could have had his choice of destination and dollars. He elected to stay at a reasonable contract which reflected his value within the league.
McDavid has competent representation. Guaranteed that before they gave him the ok to sign the deal that gave up the next 8 years (and likely most productive of his career), they discussed with him the option of waiting a year, and pursuing a more desirable place to play, with a bigger contract.
Ultimately, to do an offer sheet, Matthews would have to be somebody who is prepared to go to a team that is going to make him the highest paid player in the league, and give up first round picks in 4 out of 5 years for the privilege of doing so.
Not only is it a horrendously bad idea for that team, but it puts Matthews in the position of being the sole reason why his team cannot get success -- they're overpaying him, and they've cut out their best chances at cheaper supporting casts.
McDavid looked at that same prospect -- and while there probably wasnt an offer sheet out there which Edmonton wasnt going to match, he chose to sign a deal that was going to make him the highest paid player in the league (as he deserved to be winning the Hart in his 2nd year), but also at a term that would hopefully allow the oilers to surround him with cup-winning talent.
Matthews has the luxury of being in Toronto, where they've already got many of the elements they probably need to win a cup, so it's less of a hope.
In today's cap world, offer sheets only make sense for guys who are in marginalized situations where they are being undervalued by their existing team. Nylander could have been an example, but Dubas caved and gave him top dollar.